Question

A path 1m wide is built along the border and inside a square garden of side 30m . Find . 1). The area of path 2). The cost of planting grass in the remaining portion of the garden at the rate of ₹ 40 per m​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Measure of side of the square garden = 30 m.
• A path is built along the border and inside the garden.
• Width of the path = 1 m.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

1. The area of path.
2. The cost of planting grass in the remaining portion of garden at the rate of 40/- per m².

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(Square)}={(Side)}^{2}\:sq.units}}}$

${\underline{\underline{\bf{Solution:}}}}$

Look at the attachment! The diagram of the entire garden is given. There, the path is lying inside the garden (near the border). The width of the path is given as 1 m. And the measure of side of the entire garden is 30 m.

1) Area of path:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎As the first question, we're asked to find the area of path. Let's consider the garden is of two concentric squares. So, the area of path can be found by subtracting the area of smaller square from the area of larger square. We know the measure of side the larger square. So, first we've to find the measure of side of smaller square.

Side of smaller square:

$\rightarrow$ Side of larger square - Width of the path

$\rightarrow{\sf{30-1}}$

$\rightarrow\underline{\sf{29\:m}}$

Area of path:

$\rightarrow$ Area of larger square - Area of smaller square

$\rightarrow{\sf{{(30)}^{2}-{(29)}^{2}}}$

$\rightarrow{\sf{(30\times 30)-(29\times 29)}}$

$\rightarrow{\sf{900-841}}$

$\rightarrow{\sf{\red{\underline{\underline{59\:{m}^{2}}}}}}$

2) Cost of planting grass:

Here, we're asked to find the cost of planting grass in the remaining area. Remaining area = Area of smaller square. Cost per m² = 40/-. The product of area of smaller square and cost per m² is the required answer. In the first question, we've found the side of the smaller square. By substituting the measure of side in the formula,

$\:\:\:\:\:\:\:\:\implies{\sf{{(Side)}^{2}\:sq.units}}$

$\:\:\:\:\:\:\:\:\implies{\sf{{29}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{29\times 29}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{841\:{m}^{2}}}}}$

Now multiply the area with cost per m² (40/-)

$\rightarrow{\sf{841\times 40}}$

$\rightarrow{\sf{\red{\underline{\underline{33,640/-}}}}}$

${\underline{\underline{\bf{Final\:answer:}}}}$

• The area of the path is 59 m².
• The cost of planting grass in the remaining area is 33,640/-.

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