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 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
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.
