SOLUTION: Can you help me with this word problem?? The problem is as follows, "The area of a triangle is 27 square feet.Its height is three times the length of its base. Find the height and

Algebra ->  Equations -> SOLUTION: Can you help me with this word problem?? The problem is as follows, "The area of a triangle is 27 square feet.Its height is three times the length of its base. Find the height and       Log On


   

Question 500684: Can you help me with this word problem?? The problem is as follows, "The area of a triangle is 27 square feet.Its height is three times the length of its base. Find the height and base of the triangle." Please help. Thanks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of any triangle is 1/2 the base times the height
let the base = +b+
Let the height = +h+
given:
(1) +%281%2F2%29%2Ab%2Ah+=+27+
(2) +h+=+3b+
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Substitute (2) into (1)
(1) +%281%2F2%29%2Ab%2A3b+=+27+
(1) +%283%2F2%29%2Ab%5E2+=+27+
(1) +b%5E2+=+%282%2F3%29%2A27+
(1) +b%5E2+=+18+
(1) +b+=+3%2Asqrt%282%29+
and, since
(2) +h+=+3b+
(2) +h+=+3%2A3%2Asqrt%282%29+
(2) +h+=+9%2Asqrt%282%29+