Triangles

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GED Math › Triangles

Questions 1 - 10

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

What is the area of a right triangle if the hypotenuse is 10, and one of the side lengths is 6?

Explanation

To determine the other side length, we will need to use the Pythagorean Theorem.

Substitute the hypotenuse and the known side length as either or .

Subtract 36 from both sides and reduce.

Square root both sides and reduce.

The length and width of the triangle are now known.

Write the formula for the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the dimensions.

$A=\frac{1}{2}(8)(6) = 24$

The answer is .

What is the area of a right triangle if the hypotenuse is 10, and one of the side lengths is 6?

Explanation

To determine the other side length, we will need to use the Pythagorean Theorem.

Substitute the hypotenuse and the known side length as either or .

Subtract 36 from both sides and reduce.

Square root both sides and reduce.

The length and width of the triangle are now known.

Write the formula for the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the dimensions.

$A=\frac{1}{2}(8)(6) = 24$

The answer is .

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

The hypotenuse of a right triangle is $1285;\text{in}$ and one of its leg measures $1028;\text{in}$ . What is the length of the triangle's other leg? Round to the nearest hundredth.

$771;\text{in}$

$754.25;\text{in}$

$852.36;\text{in}$

$796.21;\text{in}$

$225.54;\text{in}$

Explanation

For this problem, you just need to remember your handy Pythagorean theorem. Remember that it is defined as:

where and are the legs of the triangle, and is the hypotenuse. Remember, however, that this only works for right triangles. Thus, based on your data, you know:

Subtracting 1056784 from each side of the equation, you get:

Using your calculator to calculate the square root, you get:

The length of the missing side of the triangle is $771;\text{in}$ .

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, what does the length of the hypotenuse need to be?

Explanation

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, what does the length of the hypotenuse need to be?

To find the length of a hypotenuse of a right triangle, simply use the Pythagorean Theorem.

Where a and b are the arm lengths, and c is the hypotenuse.

Plug in our knowns and solve.

$c=\sqrt{100ft^2}=10ft$

Note that we could also have found c by identifying a Pythagorean Triple:

3x-4x-5x

3(2)-4(2)-5(2)

6-8-10

A right triangle has hypotenuse with length 20 and a leg of length 9. The length of the other leg is:

Between 17 and 18.

Between 18 and 19.

Between 16 and 17.

Between 15 and 16.

Explanation

By the Pythagorean Theorem, if we let be the length of the hypotenuse, or longest side, of a right triangle, and and be the lengths of the legs, the relation is

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

Set and , and solve for $b^{2}$ :

$9^{2}+ b^{2} = 20^{2}$

Square the numbers - that is, multiply them by themselves:

$81+ b^{2} =400$

Subtract 81 from both sides to isolate $b^{2}$ :

$81+ b^{2} - 81 =400-81$

$b^{2} = 319$

$b=\sqrt{319}$

To find out what integers falls between, it is necessary to find the perfect square integers that flank 319. We can see by trial and error that

$17^{2}= 17 \times 17 = 289$

$18^{2}= 18 \times 18 = 324$

$17<\sqrt{319}< 18$

The length of the second leg thus falls between 17 and 18.

You are visiting a friend who has right-triangular shaped pool. You are seeing who can swim around the perimeter of the pool fastest. If the long side is 20 meters, and second shortest side is 15 meters long, how long is the shortest side?

$5\sqrt{7}m$