Question

n rectangle ABCD, length AB measures (x + 7) cm while length CD measures (3x – 5) cm. If the

breadth BC of the rectangle measures (2x – 2) cm, then show that the area of the rectangle is 130​

Answer 1

Answer:

AB = CD ( OPPOSITE SIDE OF RECTANGLE )

(x+7) =(3x -7)

x+7 = 3x -7

7+7 = 3x -x

14 = 2x

x = 7

so A AND C ARE OF 14 CM

P = 2( L+B)

130 = 2( 14 + (2x-2))

130=2( 14+ 2x-2)

130= 2(12+2x)

65 = 12 + 2x

53 = 2x

26.5 = x

so BC IS 51

and then you can calculate perimeter it will be 130

Answer 2

Answer:

Since the opposite sides of a rectangle are equal,

AB=CD and BC=AD

AB = CD

x+7 = 3x-5

Shifting the like terms:

7+5= 3x-x

12= 2x

12/2= x

x= 6 cm

length of side AB= x+7= 6+7 = 13 cm

Breadth of BC= 2x-2= 2×6- 2= 12-2= 10 cm

Area of a rectangle = Length × Breadth

AB × BC= 13×10 = 130 cm.

Hence proved.