Question

The area of a rectangle is 20 cm². The height is 4 cm longer than thrice the width.

Find the width of the rectangle.

cm

Answer 1

width = 2 cm

Explanation:

are of rectangle is equal to length times width

x is the width, then length is 3x + 4

so x(3x + 4) = 20

3x^2 + 4x = 20

3x^2 + 4x - 20 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

so a = 3

b = 4

c = -20

substitute in the formula

x = [-4 +/-√(4^2 - 4(3)(-20))]/2(3)

x = [-4 +/- √(16 + 240)]/6

x = [-4 +/- 16]/6

x1 = (-4 + 16)/6 = 2

x2 = (-4 - 16)/6 = -20/6

since the width can't be a negative number, x2 is not the right answer

so x = 2