Question

The hypotenuse of a 45°-45°-90° triangle measures 128 cm.What is the length of one leg of the triangle?

Answer 1

64sqrt2 is the exact answer. 90.51 to the hundredth or 91 to the nearest whole. The formula is hyp = sqrt2 times leg

Answer 2

Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

In 45°−45°−90° triangle

Sides are in the proportion
`1:1:√(2)`

then,

the measures of the sides are
`x , x ,√(2)x`

The length of hypotenuse=
`√(2)` times the length of the leg. ....[1]

Given: length of hypotenuse = 128 cm.

then,

from [1] we have;

128 =
`√(2)\cdot x`

or

`x=(128)/(√(2))` =
`(128)/(√(2) ) *  (√(2))/(√(2))  = (128√(2))/(√(2)\cdot √(2))`

Simplify:

`x =(128 \cdot √(2))/(2) =64√(2)` cm.

Therefore, the length of one leg of the triangle is;
`64√(2)` cm.