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 m²
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.

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