Question

Complete the following.

Answer 1

The length of the given rectangle is 2x + y + 8 and 4x - y

2x + y + 8 = 4x - y

⇒ y + y + 8 = 4x - 2x

⇒ 8 + 2y = 2x

⇒ 2x - 2y = 8

Dividing by 2

⇒ x - y = 4     ...(I)

The breadth of the rectangle is 2y and x + 4. 

2y = x + 4

⇒ x - 2y = -4     ...(II)

Subtracting (II) from (I) 

x - x - y - (-2y) = 4 - (-4)

⇒ -y + 2y = 8

⇒ y = 8

Putting the value of y = 8 in (I) we get

x - 8 = 4

⇒ x = 4 + 8 = 12

Length = 4x - y

= 4 × 12 - 8

= 40

Breadth = 2 × 8

= 16

Perimeter = 2 (length + breadth)

= 2 (40 + 16) 

= 112

Area = length × breadth

= 40 × 16

= 640 sq. units