Answer:
Step-by-step explanation:
Let x = width in ft
y= length in ft
Given, y = 3+2x ----(1)
Area = xy = 77 ft2
Using (1) to replace y
3x+2x2=77
2x2+3x-77=0
Solve this quadratic equation, a=2, b=3, c=-77
x=(-3(+or-)sqrt(32-4*2*(-77)))/(2*2)
= (-3 (+ or -) sqrt(9+616))/4
= (-3 (+ or -) sqrt(625))/4
= (-3 (+ or -) 25)/4
x = (-3+25)/4 or x = (-3-25)/4
= 22/4 = -28/4
x = 5.5 x = -7
x is the length and can't be negative. so, proceed with x= 5.5
xy = 77
y = 77/5.5 = 14
Dimensions of the rectangle are 5.5ft and 14 ft
(Check: 2* 5.5 + 3 = 11+3 = 14)