Triangles - SSAT Middle Level Quantitative

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Question

A triangle has sides feet, feet, and feet. Calculate its perimeter.

Answer

The perimeter of any figure is the sum of the lengths of the sides: .

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Question

Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?

Answer

An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.

This makes the perimeter either

or

Of our choices, we choose 38.

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Question

The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?

Answer

Since it is isosceles, 2 of the sides must be equal. They must also add to 18.

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Question

An equilateral triangle has perimeter centimeters. How long is one side?

Answer

An equilateral triangle has three sides of equal measure, so divide its perimeter by :

$73.5 \div 3 =24.5 \textrm{ cm}$

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Question

An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?

Answer

One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to $8 \times 12 + 6 = 96 + 6 = 102$ inches.

An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:

$102 \div 3 = 34$

To convert 34 inches to feet and inches:

$34\div 12 = 2 \textrm{ R }10$

One side measures 2 feet 10 inches.

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Question

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

Answer

By the Pythagorean Theorem, if and are the legs of a right triangle and is its hypotenuse, then

$a^{2} + b^{2} = c^{2}$ .

Set and solve for :

$a^{2} + 60^{2} = 65^{2}$

$a^{2} + 3,600 = 4,225$

$a^{2} + 3,600 -3,600 = 4,225 -3,600$

$a^{2} = 625$

$\sqrt{a^{2}} =\sqrt{ 625}$

The perimeter of the triangle - the sum of the sidelengths - is

.

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Question

Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

Answer

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: .

Because the lengths are in inches, the answer must be in inches as well.

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Question

What is the perimeter of an equilateral triangle with a side length ?

Answer

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

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Question

A right triangle has legs feet and feet long. What is its perimeter, in inches?

Answer

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute :

$c = \sqrt{a ^{2} + b^{2} } =\sqrt{9 ^{2} +12^{2} } = \sqrt{81+144} = \sqrt{225} = 15$ feet

Its perimeter is feet. Multiply by 12 to get the perimeter in inches:

$36 \times 12 = 432$ inches

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Question

If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?

Answer

An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.

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Question

The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?

Answer

If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.

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Question

Find the perimeter of a triangle with sides , , and .

Answer

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals . Therefore, the answer is .

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Question

What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?

Answer

Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.

$36\ \text{in}\div 12\ \text{in per ft}=3\ \text{ft}$

In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.

Add the sides together to find the total perimeter.

The perimeter of the triangle is 9 feet.

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Question

The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?

Answer

Since the triangle is an isoscles, two of the sides must be equal. They must also add to . Looking at the possibilities, only have two sides that are the same length. Now we need to check the triangle inequality to make sure the lengths create a triangle. The triangle inequality is:

Plugging into these inequalities we get:

Therefore, the inequalities hold true thus, creates a triangle. Now we need to look at the sum of the lengths:

Therefore, is the correct answer.

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Question

Find the perimeter of an equilateral triangle with a base of 11in.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.

So, we can substitute. We get

$P = 11\text{in} + 11\text{in} + 11\text{in}$

$P = 33\text{in}$

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Question

What is the area of a triangle with a base of and a height of ?

Answer

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Question

A right triangle has legs 90 centimeters and 16 centimeters, What is its area?

Answer

The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting :

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 16 \cdot 90= 720$

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Question

A triangle has base 18 inches and height 14 inches. What is its area?

Answer

Use the area formula for a triangle, setting :

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 18 \cdot14 = 126$

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Question

What is the area of the above triangle?

Answer

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

$\frac{1}{2} \cdot 7 \cdot 24 = 84$

That is, the area is 84 square inches.

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Question

What is the area of the above triangle?

Answer

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

$\frac{1}{2} \cdot 50 \cdot 120 = 3,000$

That is, the area is 3,000 square millimeters.

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