Quadratic equation

Question

One side of a rectangle is 5 inches longer than the other side. The area of the rectangle (in square inches) is three times the perimeter of the rectangle (in inches). Denote the length of the shorter side by x and then work parts (a) – (c) below.

(a) (3 points) Set up a single quadratic equation in x that captures the information above. Note: if you set up two equations or fail to use x as specified, you will receive 0 points for this part.

(b) (3 pts) Use the quadratic formula to solve the equation obtained in part (a). How many solutions did you obtain?

(c) (2 points) Use the result of part (c) to check that the area of the rectangle is indeed three times its perimeter.

Answer 1

Area = 3(Perimeter) A = 3(2L+2x) =6(L+x) = 6(x+5+x) = 12x + 30 = Area =xL = x(x+5)=x^2 +5x

x^2 +5x = 12x +30

x^2 -7x -30 = 0

x= 7/2 + or - (1/2)sqr(49+120) = 3.5 + or - .5sqr169 = about 3.5+6.5 = 10 (ignore negative sqr)

L=10+5=15

Area = 10(15) = 150

Area = 3P = 6(L+x) = 25(6)=150