# The area of a rectangle is 192 sq cm and its perimeter is 56 cm . Find the dimensions of the rectangle .

2
by khareaakanksha

• Brainly User
2015-02-03T20:03:26+05:30
The area of a rectangle = l x b = 192 cm(sq)
= l = 192/b
The perimeter = 2l + 2b = 56
= 2*(192/b) + 2b = 56
= (384/b) +2(b^2) =384
rearranging&dividing by 2 = b^2 - 28b + 192 =0
= b^2 - 16b - 12b + 192 = 0
= b(b - 16) - 12(b - 16) = 0
= (b - 16) (b -12) =0
so b-16=0 i.e b= 16
or
b-12 = 0 i.e b = 12
if l = 12 then b = 16 or vice versa

area = l * b = 12 * 16 = 192
peri = (2 *12)+(2 * 16) = 24 +52 = 56

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2015-02-03T20:19:03+05:30

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given area of rectangle = 192 sq cm
i.e., l×b = 192 ------------------ 1
given its perimeter is 56 cm
2(l+b) = 56
l+b = 28
b = 28 - l -----------------------------2
substitute 2 in 1
then we get  l(28-l) = 192
l
² - 28l + 192 = 0
l² -16l - 12l +192 = 0
l(l-16) -12(l-16) = 0
l-12 = 0 or l-16 = 0
then l= 12 or 16
by substituting them in 1 we get
12 × b = 192 or  16 × b = 192
then b = 16 or 12
hence if l=12 then b=16
or
if l=16 then b=12