Question

A rectangular grassy plot is 112 m long and 78 m broad. It has gravel path 2.5 m wide all
around it on the side. Find the area of the path and the cost of constructing it at Rs. 4.50 per
square metre.​

Answer 1

Answer:

${ \underline{ \sf{ \underline{☃Given:}}}}$

• Length of rectangular grassy plot = 112m
• Broad of rectangular grassy plot = 78m
• Cost of constructing per meter = Rs. 4.50

$\underline{ \sf{ \underline{☃Find:}}}$

• Area of the path?
• Cost of constructing?

${ \underline{ \sf{ \underline{☃Solution:}}}}$

Inner area of rectangle:-

We know that ⤵

${ \boxed{ \sf{Area \: of \: Rectangle = Length×Breadth}}}$

$\to{112 \times 78 }$

${ \to{ \red{ \sf{Inner \: area \: of \: rectangle = 8736 {m}^{2} }}}}$

width of path = 2.5m

Length of outer rectangle = 112 - (2.5 + 2.5) = 107m

Breadth of outer rectangle = 78 – (2.5 + 2.5) = 73m

Outer area of rectangle:-

$\to \sf length × breadth$

$\to \: 107 \times 73$

${ \to{ \red{ \sf{Outer \: area \: of \: rectangle = 7811 {m}^{2} }}}}$

Area of Path:-

Area of path = Area of outer rectangle - Area of inner rectangle

${ \to{ \sf{Area \: of \: path = 8736 - 7811}}}$

${ \to{ \sf{ \blue{Area \: of \: path = 925 {m}^{2} }}}}$

Cost of construction:-

From question ⤵

Cost of construction per meter ² = Rs.4.50

Cost of construction for 925m² = 925 × 4.50= 4162.5

${ \to{ \sf{ \blue{Cost \: of \: construction \: for \: 925m² =Rs 4162.5}}}}$

Hence,

Area of path = 925m²

Cost of construction = Rs 4162.5

Answer 2

Answer:

We know that, Inner area of rectangle = length × breadth Inner area of rectangle = 112 × 78 = 8736 m2 Width of path = 2.5 m Length of outer rectangle = 112 – (2.5 + 2.5) = 107 m Breadth of outer rectangle = 78 – (2.5 + 2.5) = 73 m And, Outer area of rectangle = length × breadth Outer area of rectangle = 107 × 73 = 7811 m2 Now let’s calculate Area of path, Area of path = Outer area of rectangle – Inner area of rectangle Area of path = 8736 – 7811 = 925 m2 Also given that, Cost of construction for 1 m2 = Rs 4.50 ∴ Cost of construction for 925 m2 = 925 × 4.50 = Rs 4162.5