The two shorter sides of a right triangle have the same length. The area of the right triangle is 7.07 square, what is the length of the triangle?

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The two shorter sides of a right triangle have the same length. The area of the right triangle is 7.07 square, what is the length of the triangle?

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Answer 1 · 2016-10-02T05:44:11

Each of the equal sides has a length of 3.760 and the hypotenuse has a length of 5.318

Explanation:

Uh, I don't get what exact measurement of the triangle you want so I'll give you the length of all 3 sides.

In your case you've described an isosceles right triangle. Meaning the angle between the two equal sides is 90 degrees. Since we know that the formula for the area of a triangle is $\frac{b a s e \cdot h e i g h t}{2}$ $(base * height)/2$ and we can use each of the equal sides for base and height, we get:
$\frac{s i d e \cdot s i d e}{2} = 7.07$ $(side*side)/2=7.07$ so:

$s i d e^{2} = 14.14$ $side^2=14.14$
$s i d e = \sqrt{14.14}$ $side=sqrt(14.14)$
$s i d e = 3.76$ $side=3.76$

Now to find the hypotenuse, we can use Pythagoras' Theorem that states that $s i d e 1^{2} + s i d e 2^{2} = h y p o t e n$ $side1^2+side2^2=hypoten$ $u s e^{2}$ $use^2$ or as more commonly seen $a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$

In our case a and b are equal and we know that $a^{2} = 14.14$ $a^2=14.14$ so:
$14.14 + 14.14 = c^{2}$ $14.14+14.14=c^2$
$c = \sqrt{28.28}$ $c=sqrt(28.28)$
$c = 5.318$ $c=5.318$

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The two shorter sides of a right triangle have the same length. The area of the right triangle is 7.07 square, what is the length of the triangle?

1 Answer

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