Question

The ratio of length of two rectangles is 24 : 23 and the breadth of the two rectangles is 18 : 17. If the perimeter of the second rectangle is 160 cm and the length of the second rectangle is 12 cm more than its breadth, the find the area of the first rectangle?

• A. 1700 sqcm
• B. 1728 sqcm
• C. 1628 sqcm
• D. 1180 sqcm

Answer 1

Answer:

B. 1728 sqcm

Let the length of rectangle-1 is L₁= 24x

Length of rectangle -2, L₂= 23x

breadth of rectangle -1 B₁=18y

breadth of rectangle -2 B₂=17y

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

=>2(23x+17y)=160cm

=>23x+17y=80 ----------(1)

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

L₂=12+B₂

$23x=12+17y$

$23x-17y=12$ -----------(2)

By add(1) and (2),

$46x=92$

$x=2$

sub x value in (1)

We get ., $46-12=17y$

$17y=34$

$y=2$

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

$=(24\times{2})\times({18\times{2}})$

$=48\times{36}$

$=1728cm^2$