Question

A rectangle is 10 cm long and 8 cm wide when each side of rectangle is increased by x cm, its perimeter is doubled. Find the equation in x and hence find the area of new rectangle

Answer 1

length=10cm
breadth=8cm
Perimeter=2(10+8)cm
=36cm

length=(10cm+x)
breadth=(8cm+x)
Perimeter=2(10+x+8+x)cm
=2(2x+18)cm
=4x+36cm
let 4x+36cm be equation 1

Given perimeter=2×36
=72cm
let 72 be equation 2
therefore,from equation 1 and equation 2 we get 4x+36=72
4x=72-36
x=36/4
x=9
therefore length of the new rectangle=10+9=19cm
breadth of the new rectangle= 8+9=17cm
Area of a rectangle=(l×b)
Area of the new rectangle=(19×17)cm^2

=323cm^2

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Answer 2

Given length = 10 cm
Breadth = 8 cm

Perimeter =2(10+8)=36 cm.

Givenboth increased by x

Length will be. 10+x
Breadth will be 8+x

Perimeter = 2( 10+8+2x)
=36+4x

Given perimeter is doubled

36+4x =2(36)

4x=36

x =9

Hence,
Length =10+9=19 cm

Breadth =8+9=17 cm.

Area = 19*17= 323 cm^2