Question

The area of a rectangle is 77 m2 , and the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle

Answer 1

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)