Question

5. In the figure given below, a rectangular lawn measuring 40 m x 30 m has two paths, each
5 m wide, running through the middle of it. One of the paths is parallel to the length of the
lawn while the other is parallel to the breadth. Find the cost of covering the paths with gravel
at the rate of
2 per sq m.
​

Answer 1

Answer:

Area of the rectangular lawn = 40*30 = 1200m*m

area of two paths = (40-25)(30-25) =75m*m

Area of the paths = 1200-75 =1125m*m

cost of covering the path = 1125*2= Rs2250

Answer 2

Given:-

Length of Lawn = 40 m

Breadth of Lawn = 30 m

Width of Paths = 5 m

Cost of covering the paths with gravel = ₹2/m²

Solution:-

Area of Lawn ⇒ Length × Breadth

                      ⇒ 40 m × 30 m

                      ⇒ 1200 m²

Now, Area of remaining part of lawn excluding paths ⇒ ( Length × Breadth ) - ( Side² )

                                                                         ⇒ [ (40 - 5) × (30 - 5) ] - ( 5² )

[ The place where two paths meet come two times in finding the area so, we have substract one of the square crossing ]

                                                                         ⇒ ( 35 × 25 ) - 25 m²

                                                                         ⇒ 875 - 25 m²

                                                                         ⇒ 850 m²

Area of Paths ⇒ 1200 m² - 850 m²

                       ⇒ 350 m²

∵ Rate of covering the paths with gravel at ₹2/m²

∴ Cost of covering the paths with gravel ⇒ ₹2/m² × 350 m²

                                                                   ⇒ ₹700

Hence, Cost of covering the paths with gravel is ₹700

Some important terms:-

• Area of Rectangle = Length × Breadth

• Perimeter of Rectangle = 2 ( Length + Breadth )

• Area of Square =Side²

• Perimeter of Square = 4 × side