SOLUTION: The base of a triangle is one third as long as its height. If the area of the triangle is 24 square meters, how long is its base?

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Question 109559This question is from textbook College Algebra
: The base of a triangle is one third as long as its height. If the area of the triangle is 24 square meters, how long is its base? This question is from textbook College Algebra

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The base=b of a triangle is one+third as long as its height=h.
the area=A of the triangle is 24m%5E2
b=?
since A+=+24m%5E2
b+=+1%2F3%28h%29 => h+=+3b
then
A+=+%281%2F2%29b%2Ah
24m%5E2+=+%281%2F2%29b%2A3b
24m%5E2+=+3b%5E2%2F2......divide both sides by 3
8m%5E2+=+b%5E2%2F2.........multiply both sides by 2
16m%5E2+=+b%5E2...........16+=+4%5E2

then
%284m%29%5E2+=+b%5E2.......if exponents are same then bases are same
b=4m......=> h+=+3%2A4m+=+12m
check:

A+=+%281%2F2%29b%2Ah
24m%5E2+=+%281%2F2%294m%2A12m.......multiply 4m and 12m
24m%5E2+=+%281%2F2%2948m%5E2.....divide by 2
24m%5E2+=+24m%5E2