Question

12. Two cross roads, each of width 5 m, run at 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 y of
105 per m²​

Answer 1

Answer:

550m^{2}, ₹57750

Step-by-step explanation:

Take the length of the vertical crossroad as the length of the rectangle i.e. 70m.

We know that the width is 5m.

Thus, Area of the road = l*b = 70*5 = 350m^{2}

Similarly,

Take the length of the horizontal crossroad as the breadth of the rectangle i.e. 45m.

We know that the width is 5m.

Thus, Area of the road = l*b = 45*5 = 225m^{2}

However, if we add these 2 areas, we will be counting the centre of intersection of area 5*5 twice.

Thus, area of the crossroads= (Area of 1st crossroad + Area of second crossroad) - Area of intersection

i.e 550m^{2}

So, if the cost is ₹105/m^{2},

The total cost is 550*105 = ₹57750.

Answer 2

Solution:

Given:

Two cross Road, each of width 5 ,run at right angles through centre of rectangular park of length 70 m and breadth 45 m and parallel to its sides.

Find:

Find the area of the roads . Also find the cost of constructing the roads at the rate of rupees 105 per m².

Calculations:

Area of the cross roads in the area of shaded part The area of the rectangle PQRS are the area of the rectangle EFGH. The area of the square KLMN is taken twice and this is to be subtracted.

$\sf PQ = 5 \: m \: and \: PS = 45 m. \\ </p><p>\sf EH = 5 \: m \: and \: EF = 70 m. \\ </p><p>\sf KL = 5 \: m \: and \: KN = 5 m.$

Area of the path = Area of the rectangle PQRS + area of the rectangle EFGH - Area of the square KLMN.

$\sf => PS × PQ + EF × EH - KL × KN \\ </p><p>\sf => (45 × 5 + 70 × 5 - 5 × 5) m {}^{2} \\ </p><p>\sf => (225 + 350 - 25) m {}^{2} = 550 m {}^{2}$

Therefore, cost of constructing the path = ₹105×550 = ₹ 57,750 .