Question

20. Mr. Rana bought a rectangular plot whose length is 4m more than thrice the breadth. If
the perimeter of the plot is 1128m, find the dimensions of the rectangular plot. Also, find
the cost of cementing the plot at the rate of 1000 per 100 sq. m.​

Answer 1

The cost of cementing the rectangular plot is Rs. 593600

Step by step explanation:

Given:

• The perimeter of the rectangular plot is 1128m
• The length of the rectangular plot is 4m more than thrice the breadth.

To find:

The cost of cementing the rectangular plot at the rate of Rs 1000 per 100 m sq.

So,

100 m sq. = Rs. 1000

1 m sq. = Rs 10

Now,

Cementing is done in the area. So we need to find the area of the rectangular plot.

[First, we have to find the sides of the rectangular plot]

Let the breadth of the rectangular plot be x m

ATQ, the length will be (3x+4) m

Now,

Perimeter of the rectangular plot = 2(length + breadth) units

⇒ 1128 = 2(3x+4 + x)

⇒ 1128 = 2* (4x + 4)

⇒ 1128 ÷ 2 = 4x + 4

⇒ 564 = 4x + 4

⇒ 564 - 4 = 4x

⇒ 560 = 4x

⇒ 560 ÷ 4 = x

⇒ 140 = x

∴ The breadth of the rectangular plot is = 140 m

Now, The length = (3x+4) = 3*140 + 4 = 420+4 = 424 m

Now,

Area of the rectangular plot = length * breadth unit sq.

= 140 * 424

= 59360 m sq.

Now,

Cost of cementing 1 m sq = Rs 10

So,

∴ Cost of cementing 59360 m sq. = 59360 * 10 = Rs.593600