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

Answer:

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.