Question

The dimensions of a rectangular garden were 4m by 5m. Each dimension was increased by the same amount the garden then had an area of 56M^2 find the dimension of the new garden

Answer 1

The dimension of new garden is 7 meter by 8 meter

Solution:

The dimensions of a rectangular garden were 4m by 5m

Length = 4 m

Width = 5 m

Each dimension was increased by the same amount the garden then had an area of 56 square meter

Let "x" be the amount of increase

Then,

Length = 4 + x

Width = 5 + x

Also, given that,

New area = 56 square meter

The area of rectangle is given as:

`Area = length * width`

Substituting the values we get,

`56 = (4+x)(5+x)\\\\56 = 20 + 4x + 5x + x^2\\\\x^2 + 9x + 20 - 56 = 0\\\\x^2 + 9x -36=0`

Let us solve the above equation by quadratic formula

`\text {For a quadratic equation } a x^(2)+b x+c=0, \text { where } a \\eq 0\\\\x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

Using the above formula,

`\text{For } x^2+9x-36 \text{ we get , }`

a = 1 and b = 9 and c = -36

Substituting the values of a = 1 ; b = 9 ; c = -36 in above quadratic formula we get,

`x = (-9\pm √(9^2-4\cdot \:1\left(-36\right)))/(2\cdot \:1)\\\\x = (-9\pm √(81+144))/(2)\\\\x = (-9 \pm 15)/(2)`

We get two solutions,

`x = (-9+15)/(2) \text{ or } x = (-9-15)/(2)\\\\x = 3 \text{ or } x = -12`

Since dimension cannot be negative, ignore x = -12

Thus solution is x = 3

Length = 4 + x = 4 + 3 = 7

Width = 5 + x = 5 + 3 = 8

Thus dimension of new garden is 7 meter by 8 meter