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Chapter 4: Q28. (page 139)

Find the values of x and y.

In equilateral螖DEF,m鈭�D=x+y and m鈭�E=2x-y.

Short Answer

Expert verified

The value ofx andy is 40and 20 respectively.

Step by step solution

01

Step 1. Apply definition of equilateral triangle.

An equilateral triangle is a triangle which all the three angles are equal in length, that is, 60掳.

Therefore, in 螖DEF, m鈭�D=m鈭�E=m鈭�F=60.

02

Step 2. Description of step.

Consider, m鈭�D=60.

Substitute x+yfor m鈭�Dinto m鈭�D=60and simplify.

x+y=60

03

Step 3. Description of step.

Consider, m鈭�E=60.

Substitute 2x鈭�yfor m鈭�Einto m鈭�E=60and simplify.

2x鈭�y=60

04

Step 4. Description of step.

Add x+y=60and 2x鈭�y=60, to find the value of x.

x+y+2x鈭�y=60+603x=120x=40

05

Step 5. Description of step.

Substitute 40 forx into x+y=60, to find the value of y.

40+y=60y=60鈭�40=20

Therefore, the value ofx andyis 40 and 20 respectively.

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