Mandy is building a rectangular garden pond with the area of 12ft^2. The length of pool needs to be 2 ft more than twice the wid

Question

3 years ago

7

th. What are the dimensions of the pool?

1 answer:

Genrish500 [490] · Answer 1 · 2022-05-27T22:33:22+03:00

The length of rectangular pool is 6 ft and width of rectangular pool is 2 ft.

Step-by-step explanation:

Given,

Area of rectangular pool = 12 square feet

Let,

Width of pool = w

Length of pool = l = 2w+2

Area = Length * Width

$12=(2w+2)*w\\12=2w^2+2w\\2w^2+2w-12=0$

Dividing each term by 2;

$\frac{2w^2}{2}+\frac{2w}{2}-\frac{12}{2}=0\\w^2+w-6=0\\w^2+3w-2w-6=0\\w(w+3)-2(w+3)=0\\(w+3)(w-2)=0\\$

Either,

w+3 = 0 => w=-3

Or,

w-2=0 =>w=2

As width cannot be negative, therefore,

Width of rectangular pool = 2 ft

Length of rectangular pool = 2w+2 = 2(2)+2 = 4+2 = 6 ft

The length of rectangular pool is 6 ft and width of rectangular pool is 2 ft.

Keywords: rectangle, area

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