Question

Each leg of a 45°-45°-90° triangle measures 12 cm. Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The lengths of sides Z Y and Y X are 12 centimeters. What is the length of the hypotenuse? 6 cm 6 StartRoot 2 EndRoot cm 12 cm 12 StartRoot 2 EndRoot cm

Answer 1

Answer:

$XZ=12\sqrt{2}\ cm$

Step-by-step explanation:

Pythagorean theorem: In a right triangle with legs a, b and hypotenuse c,

$a^2+b^2=c^2$

Given: ΔXYZ is right triangle with right angle Y.

Angles YZX and ZXY are 45 degrees.

ZY = YX = 12 cm

Find: XZ

Solution:

By the Pythagorean theorem,

$XZ^2=XY^2+YZ^2\\ \\XZ^2=12^2+12^2\\ \\XZ^2=144+144\\ \\XZ^2=2\cdot 144\\ \\XZ=12\sqrt{2}\ cm$

Answer 2

Answer: D

Step-by-step explanation:

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