SOLUTION: The height of a triangle is 2 centimeters less than its base. If the area of the triangle is 28 square centimeters, find the base and height of the triangle. Round to the nearest t

Algebra ->  Triangles -> SOLUTION: The height of a triangle is 2 centimeters less than its base. If the area of the triangle is 28 square centimeters, find the base and height of the triangle. Round to the nearest t      Log On


   

Question 964264: The height of a triangle is 2 centimeters less than its base. If the area of the triangle is 28 square centimeters, find the base and height of the triangle. Round to the nearest tenth of a centimeter if necessary.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
b=base; h=height=b-2cm
A=%281%2F2%29bh Substitute for h.
A=%281%2F2%29%28b%29%28b-2cm%29
28cm%5E2=%281%2F2%29%28b%29%28b-2cm%29 Multiply each side by 2.
56cm%5E2=b%5E2-2b Subtract 56 from each side.
0=b%5E2-2b-56
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 1b%5E2%2B-2b%2B-56+=+0) has the following solutons:

b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-56=228.

Discriminant d=228 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+228+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+8.54983443527075
b%5B2%5D+=+%28-%28-2%29-sqrt%28+228+%29%29%2F2%5C1+=+-6.54983443527075

Quadratic expression 1b%5E2%2B-2b%2B-56 can be factored:
1b%5E2%2B-2b%2B-56+=+1%28b-8.54983443527075%29%2A%28b--6.54983443527075%29
Again, the answer is: 8.54983443527075, -6.54983443527075. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-56+%29

ANSWER 1: The base is 8.55 cm. (This would round to 8.5cm- kept extra digit for check)
h=b-2cm=8.55cm=6.55 cm (see above)
ANSWER 2: The height is 6.55 cm.
CHECK:
A=%281%2F2%29bh
28cm%5E2=%281%2F2%29%288.55cm%29%286.55cm%29
28cm%5E2=%281%2F2%29%2856.00cm%5E2%29
28cn%5E2=28cm%5E2