A rectangle is 12 cm long and 9 cm wide. Its perimeter is doubled when each of its sides is increased by a fixed length.
What is the new length of the rectangle?
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Step-by-step explanation:
length=12cm
breadth=9cm
Perimeter=2(12+9)cm
=42cm
length=(12cm+x)
breadth=(9cm+x)
Perimeter=2(12+x+9+x)cm
=2(2x+21)cm
=4x+42cm
let 4x+42cm be equation 1
Given perimeter=2×42
=84cm
let 84 be equation 2
therefore,from equation 1 and equation 2 we get 4x+42= 84
4x=84-42
x=42/4
x=10.5
therefore length of the new rectangle=12+10.5=22.5cm
breadth of the new rectangle= 9+10.5=19.5cm
Area of a rectangle=(l×b)
Area of the new rectangle=(22.5×19.5)cm^2
438.75cm^2 is the new rectangle
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