Question

What is the length of the missing side? What is the area of the figure? Show ALL work Please!

Answer 1

We use Pitagorean equation to find the hypotenuse which is the longest side of the triangle.
$a {}^{2} + b {}^{2} = c {}^{2}$
$a = 31 - 16$
This is to find the lenght of the base of the triangle.
$a = 15$

${15}^{2} + {20}^{2} = {c}^{2}$
$225 + 400 = {c}^{2}$
$625 = {c}^{2}$
Now we need to eliminate that c squared to get the length of the hypotenuse. And we do that by taking the square root of both side of the equation.
$\sqrt{625} = \sqrt{ {c}^{2} } \\ c = 25$

Answer 2

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Find the base of the triangle
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31 - 16 = 15ft

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Formula
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a² + b² = c²

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Find missing length
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15² + 20² = c²
c² = 625
c = √625
c = 25

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Answer: The missing length is 25 ft
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