Question

The length of a rectangular flower bed is 3 feet less than its width. The area of the flower that is 70 ft.² find the dimensions of the flower bed

Answer 1

The dimensions of the flowerbed is 7 ft by 10 ft

Explanation:

Firstly, Let's assign variables.

Let the length of the flower bed be l while the width of the flower bed be w.

From the question, we know that the length is 3ft less than the width. Mathematically, this can be expressed as an equation as follows;

w = l + 3 .............................(i)

The area of the bed is 70 ft.² What this means is that the product of the length and width of the bed is 70 ft.²

Mathematically;

l × w = 70 ................................(ii)

Now substitute i into ii

⇒ l × (l + 3) = 70

`l^(2) + 3l = 70`

`l^(2) + 3l -70 = 0\\l^(2) + 10l - 7l -70 =0\\l(l+10) -7(l+10) = 0\\(l-7)(l+10) = 0\\\\l= 7 or -10`

since length cannot be negative, we only take the value of l = 7

From (i), we know that w = l + 3

substituting l = 7 here, we have w = 7+3 = 10