Question

A local park is 32 m long and its width is half of the length. It has two right-triangular grass lawns with the following dimensions. The local gardener wanted to renovate the park so he hired some men. The men agreed to work on the grass lawn at Rs. 1.2 per sq metre and put new footpath at Rs. 0.80 per sq metre. What is the total cost the gardener will have to pay after the work is done?

• A. ₹​ 431.2
• B. ₹​ 368.4
• C. ₹​ 421.8
• D. ₹​ 512

Answer 1

The correct option is A

₹​ 431.2

The two triangles have different dimensions, hence different areas.
We know thaty, area of a triangle = $\frac{1}{2}$ x Base x Height
Area of 1st triangle = $\frac{1}{2}\times 5\times 12=30m^2$
Area of the other triangle = $\frac{1}{2}\times 8\times 6=24m^2$
Total area of the triangular lawns
= 30 + 24 = $54m^2$

Cost of working on the lawns
= Rate x Total area of the lawns
= $1.2\times 54=Rs.64.8$

Length of the park, $l=32m$
Breadth of the park, $b=16m$
Total area of the park
= $l\times b$
=$32\times 16=512m^2$

Area of the footpath
= Area of the park - Area of the triangular lawns
= $512-54=458m^2$

Cost of putting new footpath
= Rate x Area of footpath
= $458\times 0.8=Rs.366.4$

Total cost = 64.8 + 366.4 = Rs. 431.2