Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs 105 per m².

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Solution

Let ABCD be the rectangular park then EFGH and IJKL the two rectangular roads with width 5 m.

Length of the rectangular park AD = 70 cm
Breadth of the rectangular park CD = 45 m
∴ Area of the rectangular park = Length x Breadth = 70 m x 45 m = 3150 m²
Area of the road EFGH = 70 m x 5 m = 350 m²
Area of the road JKIL = 45 m x 5 m = 225 m²
Clearly area of MNOP is common to the two roads.
Thus, Area of MNOP = 5 m x 5 m = 25 m²
Hence,
Area of the roads = Area (EFGH) + Area (JKIL) − Area (MNOP)
= (350 + 225 ) m²− 25 m² = 550 m²
Again, it is given that the cost of constructing the roads = Rs. 105 per m²
Therefore,
Cost of constructing 550 m² area of the roads = Rs. (105 × 550)
= Rs. 57750.

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Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs 105 per m2.

Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs 105 per m².