Find both the length and width of a rectangle using the following conditions.

Question

- The length of the rectangle is the same as the length of each side of a square.
- The length of the rectangle is 4cm more than 3 times the width of the rectangle.
- The area of the square is 66cm² more than the area of the rectangle.

Looking for a method to solve this question. Thanks!

Answer 1

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)