<PRE><B>Question 198521</B>
    The altitude of a triangle is 3/4 the length of its base. If the altitude were increased by 3 feet and the base decreased by 3 feet, the area would be unchanged. Find the length of the base and altitude.
.
Original triangle:
Let b = length of base
then
(3/4)b = altitude
Area = (1/2)b(3/4)b = (3/8)b^2
.
Changed triangle:
b-3 = length of base
(3/4)b+3 = altitude
Area = (1/2)(b-3)(3/4)b+3 = (3/8)(b-3)b+3
.
Set area equal to each other:
(3/8)b^2 = (3/8)(b-3)b+3
b^2 = (b-3)b+3
b^2 = b^2-3b+3
0 = -3b+3
-3 = -3b
1 feet = b (base of triangle)
.
Altitude:
(3/4)b = (3/4)1 = 3/4 feet (altitude)



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