help!!!!

Question

The area of a square is tripled by adding 8cm to one side and 4cm tobthe other side. What are the dimensions of the rectangle thatvwas created by enlarging the square? solve by writing a quadratic and factoring.

Answer 1

Let x be the side of the square.

The dimensions of the rectangle are l = (x + 8) and w = (x + 4).

The area of the square is x².

The area of the rectangle is (x + 8)*(x + 4).

Therefore, 3x² = (x + 8)*(x + 4).

3x² = x² + 12x + 32

2x² - 12x - 32 = 0

x² - 6x - 16 = 0

x² - 8x + 2x - 16 = 0

x(x - 8) + 2(x - 8) = 0

(x + 2)(x - 8) = 0

x + 2 = 0 and x - 8 = 0

x = - 2 and x = 8.

The negative value is negligible, the value of x = 8.

The dimensions of the rectangle are l = x + 8 = 8 + 8 = 16 cm and w = x + 4 = 8 + 4 = 12 cm.