Question

The length of a rectangle is the same as the length of each side of a square.
The length of the rectangle is 4 cm more than 3 times the width of the rectangle.
The area of the square is 66 cm? more than the area of the rectangle.
Find the length and the width of the rectangle.
You must show all your working.

Answer 1

I searched your question and here is what I found:

Step-by-step explanation:

L = 4 + 3W  (from the second condition)

 

L2 = 66 + LW (combining the first and third condition)

 

L2 = 66 + L(L-4)/3

 

3L2 = 198 + L2 -4L

 

2L2 + 4L -198 = 0

 

(2L - 18)(L + 11) = 0; discarding the negative root for lack of practicality , L = 9

 

from the first equation W = (L - 4)/3 = 5/3 = 1 2/3; 1.67

 

Hence the length of the rectangle is 9 cm and the width is 1.67 cm

 

check;        

2nd condition; L = 4 + 3*1.67 = 9 (proven)

1st and 3rd condition; 92 = 66 + 9*1.67 = 81 (proven)