SOLUTION: originally a rectangle was three times as long as it was wide. when 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an are of 90c

Algebra.Com
Question 1153710: originally a rectangle was three times as long as it was wide. when 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an are of 90cm^2. what the dimensions of the new rectangle
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
This method may seem slightly backward, but:
x, the original width
3x, the original length


Solve any way you wish. Question asks for each of the two factors.
skipping steps,...



-----length of the new rectangle
-
------width of new rectangle
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

The original dimensions x cm wide and 3x cn long.


After changing it is (x+5) cm wide and (3x-2) cm long.


The equation


    (x+5)*(3x-2) = 90


You can solve it as a quadratic equation.


I will solve it mentally.


Multiply both sides by 3


    (3x+15)*(3x-2) = 270.


Find two integer factors of the number 270 that differ by 15-(-2) = 17.


Obviously, these factors are 27 and 10.


So, 3x-2 = 10;  3x = 10+2 = 12;  x = 12/3 = 4.


ANSWER:  The dimensions of the original rectangle are 4 cm (width) and 3*4 = 12 cm (length).


RELATED QUESTIONS

Originally a rectangle is three times as long as it was wide. when 2 centimeters... (answered by ankor@dixie-net.com)
Problem: Originally, a rectangle was three times as long as it is wide. When 2 cm were... (answered by jsmallt9,richwmiller)
Originally a rectangle was twice as long as it was wide. When 5m was subtracted from its... (answered by infinity9001)
Just a random question: "Originally a rectangle was twice as long as it was wide. When 4 (answered by scott8148)
Can you please solve this for me?: I have to solve this using factoring. Originally a (answered by stanbon)
A rectangle is three times as long as it is wide. If its length and width are both... (answered by josgarithmetic)
Originally a rectangle was twice as long as its wide. When 5 m was subtracted from its... (answered by stanbon,ewatrrr)
a rectangle is three times as long as it is wide. if its length and width are both... (answered by bucky)
A rectangle is three times as long as it is wide. If its length and width are both... (answered by edjones)