Question

in a rectangle ABCD , lenth AB measures (x+9) while length CD measures (2x+1) cm . if the breadth BC measures (2x-4) cm ,then show that area of rectangle is 204 cm square​

Answer 1

Answer:

$Area \ of \ rectangle  = 204 \ cm^{2}$

Step-by-step explanation:

Given that-

ABCD is a rectangle.

We know that- opposite sides of a rectangle are equals.

Then AB = CD

and AD =BC

Given that-

AB = (x + 9)

CD = (2x + 1)

BC = (2x - 4)

But AB = CD

So, (x + 9) = (2x + 1)

x - 2x = 1 - 9

-x = -8

x = 8

So, length of rectangle = AB

                                      = x + 9

                                      = 8 + 9

Length of rectangle = 17 cm

Breadth of rectangle = BC

                                   = 2x - 4

                                   = 2(8) - 4

                                   = 16 - 4

Breadth of rectangle = 12 cm

Area of rectangle A = ?

Using formula-

Area of rectangle = Length × Breadth

A = lb

  = 17×12

$Area \ of \ rectangle  = 204 \ cm^{2}$

Hence proved.