Question 10 - Figure it out - Page 154-156 - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Question 10 A tiny park is coming up in Dhauli. The plan is shown in the figure. The two square plots, each of area g2 sq. ft., will have a green cover. All the remaining area is a walking path w ft. wide that needs to be tiled. Write an expression for the area that needs to be tiled.Now, Area to be tiled = Area of bigger rectangle – 2 × Area of square plots Since the green squares have area g2, so their side length is g Our figure becomes Total height = 𝑤+𝑔+𝑤 = 𝒈+𝟐𝒘 Total width = 𝑤+𝑔+𝑤+𝑔+𝑤 = 𝟐𝒈+𝟑𝒘 Now, Area to be tiled = Area of bigger rectangle – 2 × Area of square plots = (𝒈+𝟐𝒘) × (𝟐𝒈+𝟑𝒘)−𝟐 × 𝒈^𝟐 = 𝑔(2𝑔+3𝑤)+2𝑤(2𝑔+3𝑤)−2 × 𝑔^2 = 2g^2+3gw+4gw+6w^2−2g^2 = (2g^2−2g^2)+3gw+4gw+6w^2 = 3gw+4gw+6w^2 = 7gw+6w^2 = 𝐰(𝟕𝒈+𝟔𝒘) square units