Question

A rectangular lawn 115m long and 64 m broad has two cross paths at right angles, one 2m wide, running parallel to its length and other 2.5m wide, running parallel to its breadth. find the cost of gravelling the paths at rupees 114 per m square. Please tell step by step .

Answer 1

Answer:

Let ABCD be the rectangular field and PQRS and KLMN be the two rectangular roads with width 2 m and 2.5 m, respectively.

Length of the rectangular field, CD = 115 cm

Breadth of the rectangular field, BC = 64 m

∴ Area of the rectangular lawn ABCD = 115 m 64 m = 7360 m2

Area of the road PQRS = 115 m 2 m = 230 m2

Area of the road KLMN = 64 m 2.5 m = 160 m2

Clearly, the area of EFGH is common to both the two roads.

∴ Area of EFGH = 2 m 2.5 m = 5 m2

∴ Area of the roads = Area (KLMN) + Area (PQRS) − Area (EFGH)

= (230 m2 + 160 m2) − 5 m2 = 385 m2

Rate of gravelling the roads = Rs 60 per m2

∴ Total cost of gravelling the roads = Rs (385 60)

= Rs 23,100