Question

At the rate of * 3/- per m², cost of
painting a rectangular floor is
* 7,056/-. If the breadth of the floor
is 75% of its length, then what is the
length of the floor ?​

Answer 1

Given:

At the rate of * 3/- per m², cost of  painting a rectangular floor is  Rs.  7,056/-

To find:

The  length of the floor

Solution:

Let's assume,

"l" → the length of the rectangular floor

"b" → the breadth of the rectangular floor

It is given that the breadth is 75% of its length, so we can form an eq. as:

b = $\frac{75}{100} \times l$

$\implies b = \frac{3}{4} \times l$ ...... (i)

We know that,

The cost of painting the rectangular floor = Rs. 7056

⇒ [Area of the rectangular floor] × [rate per meter square] = Rs. 7056

⇒ [l × b] × 3 = 7056

substituting the value of b from (i), we get

⇒ $[l \times \frac{3}{4}\times l ] \times 3 = 7056$

⇒ $l^2 \times \frac{9}{4} = 7056$

⇒ $l^2 = \frac{7056 \times 4}{9}$

⇒ $l^2 = 3136$

⇒ $l = \sqrt{3136}$

⇒ $\bold{l = 56\:m}$

Thus, the length of the floor is → 56 m.

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