SOLUTION: The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer?      Log On


   

Question 176017: The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let b=base and h=height

"The base of a triangle is 8cm greater than the height" means that b=h%2B8


A=%281%2F2%29bh Start with the area of a triangle formula


42=%281%2F2%29%28h%2B8%29h Plug in A=42 (the given area) and b=h%2B8


42%2A2=%28h%2B8%29h Multiply both sides by 2.


84=%28h%2B8%29h Multiply


84=h%28h%2B8%29 Rearrange the terms.


84=h%5E2%2B8h Distribute


0=h%5E2%2B8h-84 Subtract 84 from both sides.


Notice we have a quadratic equation in the form of ah%5E2%2Bbh%2Bc where a=1, b=8, and c=-84


Let's use the quadratic formula to solve for h


h+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


h+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-84%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=-84


h+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-84%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


h+=+%28-8+%2B-+sqrt%28+64--336+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-84%29 to get -336


h+=+%28-8+%2B-+sqrt%28+64%2B336+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--336%29 as sqrt%2864%2B336%29


h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 Add 64 to 336 to get 400


h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


h+=+%28-8+%2B-+20%29%2F%282%29 Take the square root of 400 to get 20.


h+=+%28-8+%2B+20%29%2F%282%29 or h+=+%28-8+-+20%29%2F%282%29 Break up the expression.


h+=+%2812%29%2F%282%29 or h+=++%28-28%29%2F%282%29 Combine like terms.


h+=+6 or h+=+-14 Simplify.


So the possible answers are h+=+6 or h+=+-14


However, since a negative height is not possible, this means that h+=+-14 is NOT a solution


So the only answer for the height is h+=+6 which means that the height is 6 cm.


b=h%2B8 Go back to the first equation


b=6%2B8 Plug in h=6


b=14 Add. So the base is 14 cm.


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Answer:


So the base is 14 cm and the height is 6 cm