SOLUTION: Hi, I'm not doing too well in Geometry and I thought you might be able to help...I had this as a homework problem:<BR><BR> Given triangleABC = triangleDEF, DE = 10, EF = 13, DF

Question 65760: Hi, I'm not doing too well in Geometry and I thought you might be able to help...I had this as a homework problem:

Given triangleABC = triangleDEF, DE = 10, EF = 13, DF is 4 more than twice a number and AC is 8 less than 4 times the same number. What is the number?

Thanks!
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
When you write that triangle ABC = triangle DEF, I expect you mean "congruent to", in which case the corresponding sides of the two triangles are congruent (equal). This means, of course, that side DF is equal to side AC, so you can write:
2n+4 =4n-8 because DF = 2n+4 and AC = 4n-8. Simplify this and solve for n.
Subtracting 2n from both sides, you get:
4 = 2n-8 Now add 8 to both sides.
12 = 2n Finally, divide both sides by 2.
n = 6

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