Question

1. The perimeter of a rectangular campsite is 64 m and its area is 207 m2. Find the length and the breadth of the campsite.

Answer 1

$\huge{ \mathtt{ \fbox{Solution :)}}}$

Given ,

• Perimeter of rectangle = 64 m
• Area of rectangle = 207 m²

Let , the length and breadth of rectangle be x and y

We know that , the area of rectangle is given by

$\large \mathtt{ \fbox{Area = length \times breadth}}$

Thus ,

207 = x × y ----- (i)

We know that , the perimeter of rectangle is given by

$\large \mathtt{ \fbox{Perimeter =2(l + b) }}$

Thus ,

64 = 2(x + y)

64 = 2x + 2y

32 = x + y

x = 32 - y ----- (ii)

Substitute the value x in equation (i) , we get

207 = (32 - y) × y

207 = 32y - y²

y² - 32y + 207 = 0

y² - 23y - 9y + 207

y(y - 23) - 9(y - 23)

(y - 9)(y - 23)

y = 9 or y = 23

Substitute the value y in equation (ii) , we get

x = 32 - 9 or x = 32 - 23

x = 23 or x = 9

Hence , the length and breadth of the rectangle are 23 m or 9 m and 9 m or 23 m

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