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Nadya [2.5K]
3 years ago
10

I want to build a right triangular deck behind my house. The hypotenuse of the deck will be 25 feet long. The other two sides of

the deck will be equal in length. What is the length of the deck?
Imported Asset



17.68 feet

15.98 feet

10.34 feet

9.32 feet
Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

Pythagorean theorem 
25^2 = x^2 + x^2
so 625 = 2x^2
312.5 = x^2
17.68 = x
17.68 feet is your answer
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t - length of side of a triangle

The perimeter of a square: P_S=4a

The perimeter of a triangle: P_T=3t

We have the area of a triangle: A_T=16\sqrt3\ cm^2

The formula of an area of an equilateral trinagle: A_T=\dfrac{t^2\sqrt3}{4}

Substitute:

\dfrac{t^2\sqrt3}{4}=16\sqrt3    <em>multiply both sides by 4</em>

t^2\sqrt3=64\sqrt3     <em>divide both sides by \sqrt3</em>

t^2=64\to t=\sqrt{64}\to t=8\ cm

The perimeter of a triangle: P_T=3(8)=24\ cm

Substitute to the formula of a perimeter of a square:

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The formula of a diagonal of a square: d=a\sqrt2

Substitute:

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Answer:

                                                                                                                                                     

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