Share
Notifications

View all notifications
Advertisement

A Square Lawn is Bounded on Three Sides by a Path 4 M Wide. If the Area of the Path is 7/8 that of the Lawn, Find the Dimensions of the Lawn. - Mathematics

Login
Create free account


      Forgot password?

Question

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.

Solution

Let the side of the square lawn be x m.
Area of the square lawn = x2 m2
The square lawn is bounded on three sides by a path which is 4 m wide.

Area of outer rectangle = (x + 4) (x + 8) = x2 + 12x + 32
Area of path = x2 + 12x + 32 – x2 = 12x + 32
From the given information, we have:

`12x + 32 = 7/8 x^2`

`96x + 256 = 7x^2`

`7x^2 - 96x - 256 = 0`

`7x^2 - 112x + 16x - 256 = 0`

7x(x - 16) + 16(x - 16) = 0

(x - 16)(7x + 16) = 0

`x = 16, (-16)/7`

Since, x cannot be negative. So, x = 16 m.
Thus, each side of the square lawn is 16 m.

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(B) | Q: 12 | Page no. 72
Advertisement
Solution A Square Lawn is Bounded on Three Sides by a Path 4 M Wide. If the Area of the Path is 7/8 that of the Lawn, Find the Dimensions of the Lawn. Concept: Quadratic Equations.
Advertisement
View in app×