Question

A garden has an area of 264ft^2. Its length is 10 ft more than its width. What are the dimensions of the​ garden?

Answer 1

Answer:

Length = 22 ft

Width = 12 ft

Step-by-step explanation:

Let length of the garden be ' x + 10 '

Let breath of the garden be ' x '

Area of the garden = 264 ft²

Now, let's find the breath of the garden 'x'

$x(x + 10) = 264$

Distribute X through the parentheses

${x}^{2} + 10x = 264$

Move constant to left and change its sign

${x}^{2} + 10x - 264 = 0$

Write 10x as a difference

${x}^{2} + 22x - 12x - 264 = 0$

Factor out X from the expression

$x(x + 22) - 12x - 264 = 0$

Factor out -12 from the expression

$x(x + 22) - 12(x + 22) = 0$

Factor out X +22 from the expression

$(x + 22)(x - 12) = 0$

When the products of factors equals to 0 , at least one factor is 0

$x + 22 = 0$

$x - 12 = 0$

Solve for X

$x + 22 = 0$

$x = 0 - 22$

$x = - 22$

Again,

$x - 12 = 0$

$x = 0 + 12$

$x = 12$

(The dimensions can't be negative. )

So, width = 12 ft

Now, let's find the length of the garden ' X + 10 '

$x + 10$

Plug the value of X

$12 + 10$

Calculate the sum

$= 22 \: ft$

Therefore,

Length = 22 ft

Width = 12 ft

Hope this helps..

Best regards!