Question

If the hypotenuse of a 45-45-90 triangle is 13, what is the length of the legs?

Answer 1

The legs of this triangle are each of length 1 unit as they are both original sides of the unit square. That is, the legs of this 45-45-90 triangle are equal. Applying the Pythagorean theorem we find that the length of the hypotenuse is equal to the square root of 2.

Answer 2

Answer:

In a 45-45-90 triangle, the length of the hypotenuse is $\sqrt{2}$ times the length of leg.

As per the statement:

If the hypotenuse of a 45-45-90 triangle is 13 units.

To find the length of the legs.

Using above definition:

$\text{Length of Hypotenuse} = \sqrt{2} \times \text{Length of the leg}$

Substitute the given values we have;

$13 = \sqrt{2}  \times \text{Length of the legs}$

Divide both sides by $\sqrt{2}$  we have;

$\text{Length of the legs} =[tex]\frac{13}{\sqrt{2}} = \frac{13\sqrt{2}}{2}$[/tex] units

Therefore, the length of the legs is $\frac{13\sqrt{2}}{2}$[/tex] units