SOLUTION: How do I set up this word problem? The height of a triangle is 5 more than half the base of the triangle. The area of the triangle is 14 squared centimeters?

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Question 471943: How do I set up this word problem?
The height of a triangle is 5 more than half the base of the triangle. The area of the triangle is 14 squared centimeters?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The height of a triangle h is 5 more than half the base of the triangle b.
h=b%2F2%2B5

The area A of the triangle is 14 squared centimeters:

A=14cm%5E2

also

A=hb%2F2

so hb%2F2=14cm%5E2....replace h with b%2F2%2B5

%28b%2F2%2B5%29b%2F2=14cm%5E2

%28%28b%2B10%29%2F2%29b%2F2=14cm%5E2

%28b%5E2%2B10b%29%2F4=14cm%5E2

b%5E2%2B10b=14cm%5E2%2A4

b%5E2%2B10b=56cm%5E2

b%5E2%2B10b-56cm%5E2=0........use quadratic formula to find b

b+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-56%29+%29%29%2F%282%2A1%29+

b+=+%28-10+%2B-+sqrt%28+100%2B224+%29%29%2F2+

b+=+%28-10+%2B-+18%29%2F2+ ......use only positive solution because the base cannot be negative

b+=+%28-10+%2B+18%29%2F2+

b+=+8%2F2+

b+=+4cm

now find h

h=b%2F2%2B5

h=4%2F2%2B5

h=2%2B5

h=7cm



check:
A=hb%2F2

A=7cm%2A4cm%2F2

A=7cm%2A2cm

A=14cm%5E2