The dimension of a rectangular garden were 3 m by 10 m when both dimension were increased by equal amounts the area of a garden double find the dimensions of the new garden answer

The answer is 5m and 12 m.

The area of a rectangle (A) with sides a and b is: A = a * b.

We have:

a = 3 m

b = 10 m.

The initial area is: A = 3 * 10 = 30 m²

When both dimensions were increased by equal amounts (x) the area of a garden double:

A1 = a1 * b1

A1 = 2A = 2 * 30 = 60 m ²

a1 = a + x = 3 + x

b1 = b + x = 10 + x

A1 = (a + x) (b + x)

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

60 = 3 * 10 + 3 * x + 10 * x + x * x

60 = 30 + 3x + 10x + x²

0 = - 60 + 30 + 3x + 10x + x²

0 = - 30 + 13x + x²

This is the quadratic equation:

x² + 13x - 30 = 0

Let's make factors:

x² + 15x - 2x - 30 = 0

x * x + 15 * x - 2 * x - 2 * 15 = 0

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

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

So, either x + 15 = 0 or x - 2 = 0.

Thus, either x = - 15 or x = 2.

Since the dimensions cannot be negative, we will ignore the negative value.

a1 = 3 + x = 3 + 2 = 5 m

a2 = 10 + x = 10 + 2 = 12 m

The dimensions are 5 m and 12 m.