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Chapter 5: Q26 (page 170)

鈻�DECKis a parallelogram. Complete.

If DE=x+y,EC=12,CK=2x-yand KD=3x-2ythen and x=?,y=?, and the perimeter of鈻�DECK

Short Answer

Expert verified

The value of x and y is 6 and 3 respectively and the perimeter of a鈻�DECK is 42.

Step by step solution

01

Step 1. Apply property of parallelogram.

Opposite sides of a parallelogram are congruent, that is, they are equal in length.

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

x+y=2x鈭�yx=2y;3x鈭�2y=12

02

Step 2. Description of step.

Substitute 2y for x into 3x鈭�2y=12 to find the value of y.

32y鈭�2y=126y鈭�2y=124y=12y=3

03

Step 3. Description of step.

Substitute 3 for y into x=2y to find the value of x.

x=2脳3=6

04

Step 4. Description of step.

The perimeter of a parallelogram is given by

P=2DE+EC=2x+y+12=26+3+12=42

Therefore, the value of x and y is 6 and 3 respectively and the perimeter of a鈻�DECK is 42.

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