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Chapter 8: Q36. (page 289)

Find the values of x,y,and z.

Short Answer

Expert verified

The value is, x=18,y=122,z=42.

Step by step solution

01

Step 1. Given information.

The given figure is,

02

Step 2. Concept used.

The small right triangle with hypotenuse 6 is similar to the large right triangle with hypotenuse x.

So,

6x=2662=2x[multiplyeachsideby6x]x=362[divideeachsideby2]x=18

03

Step 3. Find  by Pythagoras Theorem.

y2+62=182y2=324鈭�36[subtract36fromeachside]y=288[takesquarerooteachside]y=22鈰�62鈰�2y=122

04

Step 4. Use geometric mean concept.

z is the geometric mean of 2 and 18-2,

z=2鈰�16z=42

Therefore, value is x=18,y=122,z=42.

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