Question

chanda wants to put 150 square metres of garden at her backyard. This is the maximum area of garden she can have. She wants to have a rectangular area of garden with length one metre less than 3 times with the width. Find the length and width to the nearest tenth of a metre​

Answer 1

• length: 20.7 m
• width: 7.2 m

Explanation:

Let x represent the width of the garden. Then its length is 3x-1 and its area is ...

A = LW . . . . . . . . . . . . area of a rectangle is length times width

A = (3x -1)(x) = 150

3x^2 -x = 150

x^2 -1/3x +1/36 = 50 +1/36 . . . . divide by 3 and complete the square

x -1/6 = √(50+1/36) . . . . . . . . . take the square root

x = (1 +√1801)/6 ≈ 7.2397 . . . width of Chanda's garden

The length will be ...

3x -1 = 3(1 +√1801)/6 -1 = (1 +√1801)/2 -1 = (-1 +√1801)/2 ≈ 20.7191

To the nearest tenth meter, the garden is 20.7 m long and 7.2 m wide.