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.Com
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) (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
RELATED QUESTIONS
A rectangle is 4 cm longer than it is wide. If both the length and breadth are
increased (answered by macston)
A rectangle is 4 cm longer than it is wide. If both the length and breadth are
increased (answered by josgarithmetic)
A rectangle is 5 cm. longer than it is wide. If its length and width both increased by 3... (answered by josmiceli)
A rectangle is 5 cm longer than it is wide. If the length and breadth are increased by... (answered by josgarithmetic)
Length of a rectangle is greater than its breadth by 3 CM if the length is increased by 9 (answered by josgarithmetic)
The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each... (answered by ikleyn)
the length of a rectangle is 4 cm greater than its width. If the length and the width... (answered by lwsshak3)
A rectangle is 8 cm longer than it is wide. If the width is increased by 3 cm and the... (answered by Fombitz)
The length of a rectangle is greater than its breadth by 2 cm. If the length is increased (answered by macston)