Question

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

Given :-

• Perimeter of Rectangle = 64m.
• Area of Rectangle = 207 m²

To Find :-

• Length & Breadth of Rectangle ?

Formula used :-

• Perimeter of Rectangle = 2( Length + Breadth).
• Area of Rectangle = Length * Breadth.

Solution :-

Let us Assume That, Length of Rectangle is L & Breadth is B .

Than,

→ 2(L + B) = 64 --------- Equation (1).

→ L * B = 207 ------------ Equation (2).

Solving Equation (1), we get,

→ 2(L + B) = 64

→ L + B = 32 ------------ Equation (3).

using (a - b)² = (a + b)² - 4ab we get,

→ (L - B)² = (L + B)² - 4*L*B

Putting value of Equation (3) & (2) in RHS, we get,

→ (L - B)² = (32)² - 4 * 207

→ (L - B)² = 1024 - 828

→ (L - B)² = 196

→ (L - B)² = 14²

Square - Root Both sides ,

→ (L - B) = 14 -------------- Equation (4).

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Now, Adding Equation (3) & (4) we get,

→ L + B + L - B = 32 + 14

→ 2L = 46

→ L = 23m. (Ans.)

Putting This value in Equation (3) Now,

→ 23 + B = 32

→ B = 32 - 23

→ B = 9m (Ans.)

Hence, Length of Rectangle is 23m & Breadth is 9m.

Answer 2

GIVEN:

Perimeter of the Rectangular campsite = 64m

Area of the Rectangular campsite = 207m²

TO FIND:

Length and breadth of the rectangular campsite.

SOLUTION:

We know that,

Perimeter of rectangle = 2[ l + b ]

Where, l = length and b = breadth

2 [ l + b ] = 64

==> l + b = 64/2

==> l + b = 32

==> l = 32 - b ----(1)

Area of the rectangle = l × b

==> l × b = 207m² ----(2)

Substitute eq - (1) in eq - (2)

==> (32 - b)b = 207m²

==> 32b - b² = 207

=> b² - 32b + 207 = 0

Split the middle terms

==> b² - 23b - 9b + 207 = 0

==> b(b - 23) - 9(b - 23) = 0

==> b - 23 = 0 b - 9 = 0

==> b = 23 or b = 9

Breadth is always smaller , hence b = 9

Substitute b in eq - (1)

l + (9) = 32

==> l = 32 - 9

==> l = 23cm

Therefore, the length and breadth are 23cm and 9cm respectively.