# 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
Oct 2, 2016

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 $\frac{b a s e \cdot h e i g h t}{2}$ and we can use each of the equal sides for base and height, we get:
$\frac{s i \mathrm{de} \cdot s i \mathrm{de}}{2} = 7.07$ so:

$s i {\mathrm{de}}^{2} = 14.14$
$s i \mathrm{de} = \sqrt{14.14}$
$s i \mathrm{de} = 3.76$

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

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