Question

a perimeter of a rectangle is 40 cm and its area is 96 square cm find the length and breadth of a rectangle​

Answer 1

Step-by-step explanation:

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Answer 2

$\underline{\fcolorbox{red}{pink}{ \huge{Solution :}}}$

Given ,

• Perimeter of rectangle = 40 cm

1. Area of rectangle = 96 cm²

Let , the length of rectangle be l and breadth be b

We know that , the perimeter of rectangle is given by

$\sf \large \fbox{Perimeter \: of \: rectangle = 2(l + B) }$

40 = 2(l + b)

l + b = 20

it can be written as ,

b = 20 - l ------ (i)

Also , the area of rectangle is given by

$\sf \fbox{Area = Length × breadth }$

l × b = 96

Substitute the value of b from equation (i) in equation (ii) , we get

l × (20 - l) = 96

20l - l² = 96

l² - 20l + 96 = 0

(l - 12)(l - 8) = 0

l = 12 or l = 8

Putting the value of l = 12 or l = 8 in (i) , we get

b = 20 - 12 or b = 20 - 8

b = 8 or b = 12

Hence , the length and breadth of the rectangle are 12 cm and 8 cm or 8 cm or 12 cm

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