The hypotenuse of a 45 45 90 triangle measures in

Asked by admin @ 02/10/2021 in Mathematics viewed by 298 People

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

Answered by admin @ 02/10/2021

Answer:

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 $1:1:\sqrt{2}$

then,

the measures of the sides are $x , x ,\sqrt{2}x$

The length of hypotenuse= $\sqrt{2}$ times the length of the leg. ....[1]

Given: length of hypotenuse = 128 cm.

then,

from [1] we have;

128 = $\sqrt{2}\cdot x$

$x=\frac{128}{\sqrt{2}}$ = $\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}$

Simplify:

$x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}$ cm.

Therefore, the length of one leg of the triangle is; $64\sqrt{2}$ cm.

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