Asked by Jonathan
the length of a rectangle is 1 inch greater than its width if its dimensions are doubled its area increases by 36 square inches give an equation to find its dimensions
Answers
Answered by
Reiny
original width -- x
original length -- x+1
original area = x(x+1)
new width --- 2x
new length --- 2x+2
newarea = 2x(2x+2)
2x(2x+2) - x(x+1) = 36
4x^2 + 4x - x^2 - x - 36=0
3x^2 + 3x - 36 = 0
x^2 + x - 12=0
(x+4)(x-3) = 0
x = 3 or x = -4, the latter is silly answer
original width = 3, length = 4
new width = 6, new length = 8
check:
old area = 12
new area = 48
for an increase of 36
Answer is correct!
original length -- x+1
original area = x(x+1)
new width --- 2x
new length --- 2x+2
newarea = 2x(2x+2)
2x(2x+2) - x(x+1) = 36
4x^2 + 4x - x^2 - x - 36=0
3x^2 + 3x - 36 = 0
x^2 + x - 12=0
(x+4)(x-3) = 0
x = 3 or x = -4, the latter is silly answer
original width = 3, length = 4
new width = 6, new length = 8
check:
old area = 12
new area = 48
for an increase of 36
Answer is correct!
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.