9. The figure shows a rectangle with its length and breadth as indicated. Given that the perimeter of
the rectangle is 120 cm, find the area of the rectangle.
(3x - y) cm
(2x – 3) cm
(2x + y) cm

875cm^2

Step-by-step explanation:

since opposite sides are equal

3x-y=2x+y

x=2y                                                      

y=x/2                                                                      (i)

thus new length=2x+y

=2x+(x/2)                                                              [using (i)]

=(4x+x)/2

l=5x/2                                                                   (ii)

now,

perimeter=2(l+b)=120cm

l+b=60cm            

from figure and using (ii)

[5x/2]+2x-3=60

[5x+4x-6]/2=60

9x-6=120

9x=126

x=126/9

x=14                                                                 (iii)

substitute (iii) in (i)

y=14/2

y=7                                                                  (iv)

From figure,

length=2x+y                                                   [using (iii) and (iv)]

=2x14+7

length=35cm

breadth=2x-3

=2x14-3                                                          [using(iii)]

=28-3

breadth=25cm

now,

Area=lxb

=35x25

=875cm^2

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