Question

(2) Complete the following. 2x + y + 8 Find the values of x x + 4 2y I am a rectangle. and y. 4x - y - Find my perimeter and area.​

Answer 1

Solution:

Opposite sides of a rectangle are equal.

∴ 2x + y + 8 = 4x – y

∴ 8 = 4x – 2x – y – y

∴ 2x – 2y = 8

∴ x – y = 4 …(i)[Dividingboth sides by 2]

Also, x + 4= 2y

∴ x – 2y = -4 …(ii)

Subtracting equation (ii) from (i), we get



Substituting y = 8 in equation (i), we get

x – 8 = 4

∴ x = 4 + 8

∴ x = 12

Now, length of rectangle = 4x – y

= 4(12) – 8

= 48 – 8

∴ Length of rectangle = 40

Breadth of rectangle = 2y = 2(8) = 16

Perimeter of rectangle = 2(length + breadth)

= 2(40 + 16)

= 2(56)

∴ Perimeter of rectangle =112 units

Area of rectangle = length × breadth

= 40 × 16

∴ Area of rectangle = 640 sq. units

∴ x = 12 and y = 8, Perimeter of rectangle is 112 units and area of rectangle is 640 sq. units.