Question

d) A rectangular court is twice as long as its breadth and its perimeter is 540 m. Find the number of bricks of size 20 cm x 12 cm to pave the court. If the rate of cost of bricks
is Rs 950 per 1000, find the cost of paving the court.​

Answer 1

Given:

A rectangular court is twice as long as its breadth

Its perimeter is 540 m².

If the rate of the cost of bricks  is Rs 950 per 1000

To find:

(i) Find the number of bricks of size 20 cm x 12 cm to pave the court?

(ii) Find the cost of paving the court.​

Solution:

(i). Finding the number of bricks of size 20 cm x 12 cm to pave the court:

Let's assume,

"l" → the length of the rectangular court

"b" → the breadth of the rectangular court

∴ l = 2b ..... (i) .. (given)

∴ The Perimeter of the court = 540

substituting the formula of the perimeter of a rectangle is 2(l + b)

⇒ 2 (l + b) = 540

substituting from (i)

⇒ 2 (2b + b) = 540

⇒ 2 × 3b = 540

⇒ 6b = 540

⇒ b = 90 m

∴ l = 2b = 2 × 90 = 180 m

Dimension of each brick:

length = 20 cm = 0.2 m

breadth = 12 cm = 0.12 m

Now,

The required no. of bricks are,

= $\frac{Area\: of \:the\:rectangular\:court}{Area \:of \:each\:brick}$

= $\frac{180\times 90}{0.2\times0.12}$

= $\frac{16200}{0.024}$

= $\bold{675000}$

Thus, the number of bricks of size 20 cm x 12 cm to pave the court is 675000.

(ii). Finding the cost of paving the court:

If the rate of the cost of 1000 bricks is Rs. 950

Then, the rate of the cost of 675000 bricks = $\frac{950}{1000} \times 675000$ = $\bold{Rs.\: 641250}$

Thus, the cost of paving the court is Rs. 6,41,250.

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