Question

Find the width of the gravel path

Answer 1

Answer:

Now we have that Length and breadth of the rectangular field. Area of rectangle is given by Length × breadth. Now let us consider the width of gravel is x. Then we can say that length of the flower bed is 50 – 2x and breadth of the flower bed is 40 – 2x. hence we can find Area of the flower bed. Now Area of gravel path + Area of flower bed = Area of the total field. Hence we will have Area of flower bed as well as the area of gravel path. Now know the total cost of laying flower bed and gravelling the path at Rs 30 and Rs 20 per square metres is Rs 52000. Hence using this condition we will get an equation in x. Hence we will solve it to find the width of the gravel path.

Complete step by step answer:

Now we know that the dimension of the rectangular field is 50m by 40m

This means the length of a rectangular field is 50m.

And the breadth or rectangular field is 40m.

Now we know that area of the rectangle is given by length × breadth. Hence we can say

Area of a rectangular field is 50 × 40 = 200sq m ………………… (1)

Now Let us say that the width of the gravel is ‘x’ m

Hence we get the length of the flower bed is 50 – x – x = 50 – 2x.

Similarly, we have the breadth of flower bed is 40 – x – x = 40 – 2x.

Now Area of the flower bed is (50 – 2x) × (40 –

Now dividing the whole equation by 4 we get

x2−45x+200=0

⇒x2−5x−40x+200=0⇒x(x−5)−40(x−5)=0⇒(x−40)(x−5)=0

Hence x = 40 or x = 50.

Now we have the width of the rectangular field as 40 hence x cannot be 40.

Hence x = 5.

Hence the width of gravel is 5m.

Step-by-step explanation:

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