ISEE Middle Level Quantitative Reasoning - How to find the perimeter of a triangle

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

Explanation

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

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the perimeter of the roof of the skyscraper.

Explanation

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the perimeter of the roof of the skyscraper.

To find the perimeter of a triangle, we need to know the lengths of all three sides.

We know two, and we know that it is a right triangle. If you are really savvy, you can see that this must be a 45/45/90 triangle, and therefore, the remaining side must be $50\sqrt{2}m$ .

You can also find this via Pythagorean Theorem:

$c=\sqrt{5000}m=\sqrt{50^2*2}m=50\sqrt{2}m$

Next, add it all up to get:

$50m+50m+50\sqrt{2}=50m+50m+70.7m=170.7m$

Note that we rounded slightly, but our answer choices take this into account.

Find the perimeter of a right triangle, whose two legs are 5 and 12.

Explanation

To solve, you must first use the Pythagorean Theorem to solve for the hypotenuse and then add that value to the two perimeter values given.

Thus,

$c^2=a^2+b^2\Rightarrow c=\sqrt{a^2+b^2}$

$c=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$

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

$432 \textrm{ in}$

$252 \textrm{ in}$

$216 \textrm{ in}$

$504 \textrm{ in}$

$864 \textrm{ in}$

Explanation

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

Find the perimeter of an equilateral triangle with a base of length 34in.

$102\text{in}$

$68\text{in}$

$76\text{in}$

$94\text{in}$

$51\text{in}$

Explanation

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 triangle is 34in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 34in.

Knowing this, we can substitute into the formula. We get

$P = 34\text{in} + 34\text{in} +34\text{in}$

$P = 102\text{in}$

Find the perimeter of an equilateral triangle with a base of 14in.

$42\text{in}$

$28\text{in}$

$36\text{in}$

$48\text{in}$

$\text{There is not enough information to solve the problem.}$

Explanation

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 triangle is 14in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 14in. So, we can substitute.

$P = 14\text{in} + 14\text{in} + 14\text{in}$

$P = 42\text{in}$

Find the perimeter of an equilateral triangle with a base of length 7 inches.

$21\text{in}$

$21\text{in}^2$

$49\text{in}$

$49\text{in}^2$

$\text{There is not enough information to solve the problem.}$

Explanation

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

$\text{perimeter of triangle} = a+b+c$

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

So, we know the base of the triangle has a length of 7 inches. Because it is an equilateral triangle, we know that all sides are equal. Which means all sides are 7 inches. Knowing this, we can substitute into the formula. We get

$\text{perimeter of triangle} = 7\text{in} +7\text{in} +7\text{in}$