Question

Two cross roads, each of width 5 m, run at the right angles through the centre of a
rectangular park of length 70 m and breadth 45 m and 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

Answer 1

${\huge{\boxed{\underline{\mathrm{\blue{A}{\purple{n}{\red{s}{\green{w}{\pink{e}{\orange{r:-}}}}}}}}}}}$

Area of the roads = 550 m²

Cost of constructing path = ₹57, 750

Step-by-step explanation:

${\large{\boxed{\underline{\mathrm{\green{Given :-}}}}}}$

• Length of the park = 70 m
• Breadth of the park = 45 m
• Width of the roads = 5 m
• Cost of constructing roads per meter² = ₹105

${\large{\boxed{\underline{\mathrm{\orange{To \ Find :-}}}}}}$

• Area of the roads
• Cost of constructing the roads at the rate of Rs.105 per m²

${\large{\boxed{\underline{\mathrm{\blue{Solution :-}}}}}}$

Area of the crossroads is the shaded region, as shown in the attachment. Area of rectangle PQRS and the Area of rectangle EFGH is the area of the cross roads. But while doing this, area of square KLMN is taken twice, which is to be subtracted.

Now,                  PQ = 5 m and PS = 45 m

                          EH = 5 m and EF = 70 m

                          KL = 5 m and KN = 5 m

Area of the path = (Area of the rectangle PQRS + Area of the rectangle EFGH) - Area of square KLMN

$\Longrightarrow {\mathsf{(PS \times PQ + EF \times EH) - KL \times KN}}\\\\\Longrightarrow {\mathsf{((45 \times 5 + 70 \times 5) - 5 \times 5) \ m^2}}\\\\\Longrightarrow {\mathsf{((225 + 350) - 25) \ m^2}}\\\\\Longrightarrow {\mathsf{(575 - 25) \ m^2}}\\\\\Longrightarrow {\mathsf{550 \ m^2}}$

$\therefore {\boxed{\underline{\mathsf{\orange{Area \ of \ the \ paths = \ }}{\green{\mathsf{550 \ m^2}}}}}}$

Cost of constructing the path = Cost of constructing path per meter² × Area of the paths

$\longmapsto {\mathsf{Rs. \ 105 \times 550}}\\\\\longmapsto {\mathsf{Rs. \ 57, 750}}$

$\therefore {\boxed{\underline{\mathsf{\pink{Cost \ of \ constructing \ the \ paths = \ }}{\blue{\mathsf{Rs. \ 57, 750}}}}}}$

Answer 2

Answer:

➥57,750.

Step-by-step explanation:

➥see in attachment

➥hope its helps you .