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Chapter 5: Q25 (page 170)

Quad. DECK is a parallelogram. Complete.

If KT=2x+y,DT=x+2y,TE=12and TC=9, thenx=? andy=?

Short Answer

Expert verified

The value of x and y is 5 and 2 respectively.

Step by step solution

01

Step 1. Consider the following diagram.

02

Step 2. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

In a given figure, by the property of a parallelogram,

x+2y=9;2x+y=12

03

Step 3. Description of step.

Multiply equation 2x+y=12by 2.

22x+y=2脳124x+2y=24

04

Step 4. Description of step.

Subtract x+2y=9from 4x+2y=24.

4x+2y鈭�x鈭�2y=24鈭�93x=15x=5

05

Step 5. Description of step.

Substitute 5 for x into 2x+y=12 to find the value of y.

2脳5+y=1210+y=12y=12鈭�10=2

Therefore, the value of x and y is 5 and 2 respectively.

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