SOLUTION: He gave us a question he made up and told us chapter 11 would help us, but I'm not having any luck. The height of a triangle is 5 centimeters longer than three times its base. Fi

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Question 113055This question is from textbook beginning and intermediate algebra
: He gave us a question he made up and told us chapter 11 would help us, but I'm not having any luck.
The height of a triangle is 5 centimeters longer than three times its base. Find the base of the triangle if its area is 6 square centimeters. This question is from textbook beginning and intermediate algebra

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the formula for the area of a triangle is:
A+=+%281%2F2%29b%2Ah
Or
A+=+b%2Ah%2F2
Given:
A+=+6cm%5E2
h+=+5cm+%2B+3b
Then

A+=+b%2Ah%2F2%29
6cm%5E2=+b%285cm+%2B+3b%29+%2F2
6cm%5E2+=+%285bcm+%2B+3b%5E2%29+%2F2….multiply both sides by 2
12cm%5E2+=+5bcm+%2B+3b%5E2….

3b%5E2+%2B+5bcm++-12cm%5E2+=+0+….now use sqrt formula to find only positive root

b%5B1%5D=%28-5+%2B+sqrt+%285%5E2+-4%2A3%2A%28-12%29+%29%29+%2F+%282%2A3%29
b%5B1%5D=%28-5+%2B+sqrt+%2825+%2B+144+%29%29+%2F+6
b%5B1%5D=%28-5+%2B+sqrt+%28169+%29%29+%2F+6
b%5B1%5D=%28-5+%2B+13+%29+%2F+6
b%5B1%5D=+8++%2F+6
b%5B1%5D=+1.33cm

Then
h+=+5cm+%2B+3b
h+=+5cm+%2B+3%281.33cm%29
h+=+5cm+%2B+3.99cm%29
h+=++8.99cm%29
check:
A+=+b%2Ah%2F2
A+=+%281.33%2A8.99%29%2F2
A+=+%2811.96%29%2F2
A+=+5.98cm%5E2=+6cm%5E2