Question

What is the perimeter?

Answer 1

Answer:

180 inches.

Step-by-step explanation:

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Perimeter of a triangle is:

$P = a + b + c\\\rule{150}{0.5}\\a, b, c \text{ - given side lengths of a triangle}$

We would actually need to use another formula before calculating the perimeter.

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There is one missing side measure.

Since the triangle given is a right triangle, we can use the Pythagorean Theorem to solve for the third side. Since the third side is opposite the right angle, it will be the hypotenuse. The other sides will be the legs, 'a' and 'b'.

$a^2 + b^2 = c^2\\\rule{150}{0.5}\\30^2 + 72^2 = c^2\\\\\rightarrow 30^2 = 900\\\rightarrow 72^2 = 5184\\\\5184 + 900 = c^2\\\\6084 = c^2\\\\\sqrt{6084}= \sqrt{c^2}\\\\\boxed{78 = c}$

Side C is 78 inches.

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As mentioned before, the perimeter of a triangle is:

$P = a + b + c\\\rule{150}{0.5}\\a, b, c \text{ - given side lengths of a triangle}$

We are given the measurements of 30, 72, and 78 inches.

$P = a + b + c\\\rule{150}{0.5}\\P = 30 + 72 + 78\\\\\boxed{P = 180}$

The perimeter of the given triangle should be 180 inches.

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Hope this helps!