SOLUTION: a rectangle is 4 cm longer than its width. if both the length and breadth are increased by 1 cm, the area would be increased by 18 cm squared. find the length and breadth of the re

Algebra ->  Rectangles -> SOLUTION: a rectangle is 4 cm longer than its width. if both the length and breadth are increased by 1 cm, the area would be increased by 18 cm squared. find the length and breadth of the re      Log On


   

Question 800108: a rectangle is 4 cm longer than its width. if both the length and breadth are increased by 1 cm, the area would be increased by 18 cm squared. find the length and breadth of the rectangle?
im struggling to do this question, please help! thanks
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let w be the width of the rectangle and
w+4 is the length
w*(w+4) = A, where A is the area of the rectangle,
(w+1)*(w+5) = A+18
from our first equation we have w^2 +4w = A
from our second equation we have w^2 +6w +5 = A +18
now substitute for A in the second equation
w^2 +6w +5 = w^2 +4w +18
now we can subtract w^2 from both sides of the =
6w +5 = 4w +18
subtract 4w from both sides of =
2w = 13
w = 6.5 cm and length is 10.5cm
now check the answer
6.5 * 10.5 = 68.25 cm^2 and
7.5 * 11.5 = 86.25 cm^2
86.25 - 68.25 = 18 cm^2 as required