Question

Solve each data for x: (a) a rectangle has (2x + 1) and (x +2) as length and width. Its area is 77 (b.) a triangle has (2x+2) and (x+3) as base and height. Its area is 35

Answer 1

Area of a rectangle: A= Length*width
(2x+1)(x+2)=77
2x^2+4x+x+2=77
2x^2+5x+2=77
2x^2+5x-75=0
(x-5)(2x+15)=0
x=5 or x=-7.5
Length cannot be negative, so x=5 only
the length is 11, the width is 7
Next, let's look at the triangle.
Area of a triangle: A=1/2 of base*height
(1/2)(2x+2)(x+3)=35
2x^2+8x+6=70
2x^2+8x-64=0
x^2+4x-32=0
(x-4)(x+8)=0
x=4
the base is 10, the height is 7