# How do you find the length of the legs of a 45°-45°-90° triangle with a hypotenuse of 4* sqrt 2 cm.?

Dec 10, 2015

The two legs are long $4$.

#### Explanation:

If $A B$ and $B C$ are the legs, then you know that

$A {B}^{2} + B {C}^{2} = A {C}^{2}$

Since we have a ${45}^{\circ}$ - ${45}^{\circ}$ - ${90}^{\circ}$ triangle, the triangle is isosceles, and so the two legs are equal. This means that the formula becomes

$2 A {B}^{2} = A {C}^{2}$

And we know that $A C = 4 \sqrt{2}$, so $A {C}^{2} = 16 \cdot 2 = 32$. Thus,

$2 A {B}^{2} = 32$

$A {B}^{2} = 16$

$A B = 4$