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A rectangle has one side that is 6 cm shorter than the other...

A rectangle has one side that is 6 cm shorter than the other. The area of the rectangle will increase by 68 cm2 if we add 2 cm to each side of the rectangle. Find the length of the shorter side

A.

15 cm

B.

19 cm

C.

13 cm

D.

21 cm

Correct answer is C

Let the length of the longer side = x cm

∴ The length of the shorter side = (x - 6) cm

If we increase each side's length by 2 cm, it becomes

(x + 2) cm and (x - 4) cm respectively

Area of a rectangle = L x B

A1=x(x6)=x26x

A2=(x+2)(x4)=x24x+2x8=x22x8

A1+68=A2 (Given)

x26x+68=x22x8

x2x26x+2x = -8 - 68

⇒ -4x = -76

x = 764 = 19cm

∴ The length of the shorter side = x - 6 = 19 - 6 = 13 cm