The dimensions of a rectangular garden were 3m by 10 m. When both dimensions were increased by equal amounts, the area of the garden doubled. Find the dimensions of the new garden

5m by 12m

Step-by-step explanation:

Let A represent the area, L, the Length and W, the width of the garden with dimension 3m by 10m

Area of a rectangle, A = LW

Area of the garden with the old dimension = 3 (10) = 30 sq meters

Let A1 represent the area, L1 represent the length and W1, the width of the new dimension of the garden

Since the dimensions were increased by equal amounts, lets call this amount x, the area of the garden doubled

This means,

A1 = 2A

Put in the value of A

A1 = 2 (30)

A1 = 60 sq units

and

L1 = L + x

W1 = W + x

Therefore, to find the new area, we have;

A1 = (L + x) (W+x)

60 = (3 + x) (10 + x)

expand the bracket

60 = 30 + 3x + 10x + x^2

60 = 30 + 13x + x^2

Subtract 30 from both sides

60 - 30 = 30 - 30 + 13x + x^2

30 = 13x + x^2

Equate to zero to form a quadratic equation

x^2 + 13x - 30 = 0

Now, lets think of two numbers that when multiplied they give - 30 and when summed give + 13

Yes! it's + 15 and - 2

Noe lets solve the equation

x^2 + 15x - 2x - 30 = 0

x (x + 15) - 2 (x + 15) = 0

(x - 2) (x + 15) = 0

x - 2 = 0

x = 2

x + 15 = 0

x = - 15

Since we can only use the positive value of x, therefore x = 2m

To get the new dimension

Remember that;

L1 = L + x

slot in the value of L

L1 = 3 + 2

L1 = 5m

slot in the value of W

W1 = W + x

W1 = 10 + 2

W1 = 12m

Hence, the new dimension is 5m by 12m