A triangle has a base that is 65% of its height. If the base were decreased by 13 inches, how would the height need to change to keep the same proportions?
Correct Answer: D
Your Answer:
Explanation
D
The question asks for the change in a value given a proportion. Use the Geometry Basic Approach. Start by drawing two triangles, one with a smaller base than the other. The question asks about the height, so draw a line for the height. This figure should look something like this:
Next, label the figure with the information given. Since no specific numbers are given for the base and the height, plug in. Make the height of the larger triangle 100, so the base would be 65% of 100 or just 65. If the base decreases by 13 inches, the new base would be 65 - 13 = 52 inches.
Label this information on the figure, which now looks like this:
Since the base is smaller and the proportions stay the same, the height must also be smaller. Eliminate (A) and (B) because they would both make the height larger. To find the length of the new height, set up a proportion for 
: 
. Cross-multiply to get (100)(52) = (65)(x). Simplify both sides of the equation to get 5,200 = 65x. Divide both sides of the equation by 65 to get 80 = x. Since the original height was 100, the change is 100 - 80 = 20. The new height is less than the original height, so it decreased by 20. The correct answer is (D).
