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

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