SOLUTION: The area of a rectangle is 243 in^2. If the base is reduced to one-third its original length and the height is doubled, what would its new area be?

Question 614900: The area of a rectangle is 243 in^2. If the base is reduced to one-third its original length and the height is doubled, what would its new area be?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
area of a rectangle is 243 square inches.
the formula for area is length * width which can also be expressed as base * height.
we have b * h = a1
we have 1/3 * b * 2 * h = a2
this simplifies to:
2/3 * b * h = a2
the ratio of a2 / a1 is equivalent to:
(2/3 * b * h) / (b * h)
Since b*h in the numberator and b*h in the denominator cancel out, then the resulting ratio of a2 / a1 is equal to 2/3
this means that a2 is equal to 2/3 * a1
since a1 = b * h and b * h = 243, this means that the new area is equal to 2/3 * 243 which make it equal to 162 square inches.
it shouldn't really matter what b is and what h is.
example:
assume b = 10 inches.
this means that h = 243/10 = 24.3 inches.
the area is 10 * 24.3 = 243 square inches.
now we take 1/3 * the base to get 1/3 * 10 = 3.33333333 inches
we take 2 times the height to get 48.6 inches.
3.33333333 * 48.6 = 162 square inches.
assume b = 20 inches.
this means that h = 243/20 = 12.15 inches.
20 * 12.15 = 243 square inches.
1/3 * 20 = 6.6666667 inches.
12.15 * 2 = 24.3 inches.
6.6666667 * 24.3 inches = 162 square inches.
everything checks out.
the new area would be 162 square inches.

RELATED QUESTIONS
The area of a triangle is 243 in2. If both its length and width are reduced to one-third... (answered by Alan3354)

the area of a triangle is 243in squared ,if both its length and width are reduced to one... (answered by ewatrrr)

the length of a rectangle is twice its width .if the width is reduced by 1cm and the... (answered by stanbon)

The length of a rectangle is twice its width. If the width is reduced by 1 cm and the... (answered by Manan28IN,mananth)

The area of a triangle is 24 square inches. Find the height and base if its height is... (answered by josgarithmetic)

Hi If the area of a rectangle is reduced by 54cm^2 then either the length is reduced by... (answered by josgarithmetic,greenestamps)

1. If the lenght of a rectangle is doubled, does the area double? Why or why not? 2.... (answered by ptaylor)

A rectangle is twice as long as it is wide. If its length and width are each reduced by 1 (answered by amoresroy)

What is the effect on the area of a triangle if the base is doubled and the height is cut (answered by richwmiller)