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Mensuration | Mensuration Exercise 20B

Question 1

A rectangle plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. He rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at ₹ 80per m^{2} and laying the grass at ₹ 40 per\mathrm{m}^{2}.

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Let ABCD be the given grassy plot and let EFGH be the inside boundary of the path,

Then,

Length AB = 95 m

Breadth BC = 72 m

Area of the plot ABCD = (95 × 72)\mathrm{m}^{2}

=6840 \mathrm{m}^{2}

Width of the path = 3.5 m

∴EF = (95 – (2 × 3.5)) = (95 – (7)) =88 m

and FG = (72 – (2 × 3.5)) = (72 – (7)) = 65 m

Area of the rect. EFGH = (88 × 65)\mathrm{m}^{2}

=5720 \mathrm{m}^{2}

Area of the gravel path = ( area ABCD) – (area EFGH)

= (6840 – 5720)

=1120 \mathrm{m}^{2}

Rate of constructing the path = ₹ 80 per\mathrm{m}^{2}

∴Total cost of constructing the path = ₹ (1120 × 80)

= ₹ 89600

Rate of laying the grass on the plot EFGH = ₹ 40 per\mathrm{m}^{2}

∴Total cost of laying the grass on the plot = ₹ (5720 × 40)

= ₹ 228800

∴ the total expenses involved in constructing the path = ₹ (89600 + 228800)

= ₹ 318400

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Question 1

A rectangle plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. He rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at ₹ 80per m^{2} and laying the grass at ₹ 40 per\mathrm{m}^{2}.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Let ABCD be the given grassy plot and let EFGH be the inside boundary of the path,

Then,

Length AB = 95 m

Breadth BC = 72 m

Area of the plot ABCD = (95 × 72)\mathrm{m}^{2}

=6840 \mathrm{m}^{2}

Width of the path = 3.5 m

∴EF = (95 – (2 × 3.5)) = (95 – (7)) =88 m

and FG = (72 – (2 × 3.5)) = (72 – (7)) = 65 m

Area of the rect. EFGH = (88 × 65)\mathrm{m}^{2}

=5720 \mathrm{m}^{2}

Area of the gravel path = ( area ABCD) – (area EFGH)

= (6840 – 5720)

=1120 \mathrm{m}^{2}

Rate of constructing the path = ₹ 80 per\mathrm{m}^{2}

∴Total cost of constructing the path = ₹ (1120 × 80)

= ₹ 89600

Rate of laying the grass on the plot EFGH = ₹ 40 per\mathrm{m}^{2}

∴Total cost of laying the grass on the plot = ₹ (5720 × 40)

= ₹ 228800

∴ the total expenses involved in constructing the path = ₹ (89600 + 228800)

= ₹ 318400

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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