Length of a
rectangle is

*a+5*while the width is*2a-2*. If the area is 14cm, find its perimeter.__Solution__

Area = length
x width

14 = (a+5) x
(2a-2)

(a+5) (2a-2) =
14

2a

^{2}– 2a + 10a – 10 = 14
2a

^{2}+ 8a – 10 = 14
2a

^{2}+ 8a – 10 - 14 = 0
2a

^{2}+ 8a - 24 = 0 - - - - - - - (i)
We are going
to solve equation (i) by factorization.

2a

^{2}+ 8a - 24 = 0
2a

^{2}+ 12a – 4a - 24 = 0 [splitting 8a into 12a-4a]
(2a

^{2}+ 12a) – (4a – 24) = 0
2a(a + 6) – 4(a
+ 6) = 0

(2a - 4)(a + 6) = 0

2a – 4 = 0 OR
a + 6 = 0

a = 2 OR a =
-6

Length = a+5

= 2+5

= 7

Width = 2a-2

= 2(2)- 2

= 4 – 2

= 2

Perimeter =
2(length + width)

Perimeter =
2(7 + 2)

= 2 x 14

= 28

__Hence perimeter is 28cm__

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