Question

Two cross-roads 5m wide run parallel to the sides of a rectangular garden of length 45 m and width
40 m. Find the area of the cross-roads and also the cost of constructing these cros​

Answer 1

Answer:

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

Given that length of rectangular park = 70m

Breadth of rectangular park = 45m

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

Now, Area of the road JKIL = 45 m x 5 m

= 225 m2

From the figure, it is clear that area of MNOP is common to the two roads.

Thus, Area of MNOP = 5 m x 5 m = 25 m2

Therefore,

Area of the roads = Area of EFGH + Area of JKIL – Area of 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 x 550)

= Rs. 57750.

Answer 2

Question:

Two cross roads each 3 m wide, cut at right angles through the centre of a rectangular park 72 m by 56 m, such that each is parallel to one of the sides of the rectangle. The area of the remaining portion of the park is :

Answer:

Area of first cross road which is rectangle = l×b

Hence area =72m×3m=216m²

Area of 2nd cross road which is rectangle =

=56m×3m=168m²

Area of middle part which is square =3m×3m=9m²

Area of cross roads =(216+168)m²

−9m²

=384m² −9m² =375m²