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Levart [38]
2 years ago
9

What is the perimeter?

Mathematics
1 answer:
Jobisdone [24]2 years ago
8 0

Answer:

180 inches.

Step-by-step explanation:

============================

<em>Perimeter of a triangle is:</em>

<em></em>

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

We would actually need to use <em>another </em>formula before calculating the perimeter.

============================

There is one missing side measure.

Since the triangle given is a right triangle, we can use the <u><em>Pythagorean Theorem</em></u> to solve for the third side. Since the third side is opposite the right angle, it will be the <u><em>hypotenuse</em></u>. 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}

<em>Side C is 78 inches.</em>

============================

<em>As mentioned before, the perimeter of a triangle is: </em>

<em></em>

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}

<em>The perimeter of the given triangle should be 180 inches. </em>

============================

Hope this helps!

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