Question

# Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

Hint:

### Applying the property of a rectangle equates the lengths of opposite sides of the rectangle .

## The correct answer is: y=12 and z=8

### Ans :- y = 12 and z = 8

Explanation :-

Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm.

Step 1:- form the system of linear equations using the given condition

AB = CD (opposite sides of the rectangle are equal.)

— Eq1

BC = DA(opposite sides of the rectangle are equal.)

— Eq2

Step 2:- substitute the Eq1 in Eq2.

∴ z = 8

Step 3:- the value of z in Eq1.

∴ y = 12

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