Question

The hypotenuse of a 45°-45°-90° triangle measures 18 cm. A right triangle is shown. The other 2 angle measures are 45 degrees. The length of the hypotenuse is 18 centimeters. What is the length of one leg of the triangle? 9 cm 9 StartRoot 2 EndRoot cm 18 cm

Answer 1

Answer:

$9 \sqrt{2}\ cm$

Step-by-step explanation:

Given

Hypotenus = 18cm

Required

Find the length of the other two sides

From the question, we understand that the other two sides are equal; let's represent them with x.

Pythagoras theorrem states that:

$Hypotenuse^2 = x^2 + x^2$

Substitute 18 for Hypotenuse

$18^2 = x^2 + x^2$

$18^2 = 2x^2$

$18 * 18 = 2x^2$

$324 = 2x^2$

Divide both sides by 2

$\frac{324}{2} = \frac{2x^2}{2}$

$162 = x^2$

Take root of both sides

$\sqrt{162} = \sqrt{x^2}$

$\sqrt{162} = x$

$x = \sqrt{162}$

$x = \sqrt{81 * 2}$

Split the above

$x = \sqrt{81} *\sqrt{2}$

$x = 9 *\sqrt{2}$

$x = 9 \sqrt{2}$

Hence, the length of one leg is $9 \sqrt{2}\ cm$