Question

The ratio of length of two rectangles is 22 : 25 and the breadth of the two rectangles is 9 : 11. If the perimeter of the second rectangle is 160 cm and the length of the second rectangle is 14 cm more than its breadth, the find the area of the first rectangle?

• A. 1028 sqcm
• B. 1728 sqcm
• C. 1296 sqcm
• D. 1300 sqcm

Answer 1

Answer:

C. 1296 sqcm

Let the length of rectangle-1 is L₁= 22x

Length of rectangle -2, L₂= 25x

breadth of rectangle -1 B₁=9y

breadth of rectangle -2 B₂=11y

Perimeter ofsecond rectangle = 2(L₂+B₂)=160cm

=>2(22x+11y)=160cm

=>22x+11y=80 ----------(1)

Length of Second rectangle is 12cm more than its breadth.

L₂=14+B₂

$25x=14+11y$

$25x-11y=14$ -----------(2)

By add(1) and (2),

$47x=94$

$x=2$

sub x value in (2)

We get ., $50-14=11y$

$11y=36$

$y=\frac{36}{11}$

Area of Rectangle -1 $A_1=L_1\times{B_1}$

$=(22\times{2})\times({9\times{\frac{36}{11}}})$

$=4\times{9\times{36}}$

$=1296cm^2$