SOLUTION: In right triangle ABC, side AB is longer than side BC. The boxed numbers represent the possible side lengths of triangle ABC. Identify three boxed numbers that could be the side le

Algebra ->  Triangles -> SOLUTION: In right triangle ABC, side AB is longer than side BC. The boxed numbers represent the possible side lengths of triangle ABC. Identify three boxed numbers that could be the side le      Log On


   

Question 1127994: In right triangle ABC, side AB is longer than side BC. The boxed numbers represent the possible side lengths of triangle ABC. Identify three boxed numbers that could be the side lengths of triangle ABC. Select the number you choose to represent the length of each side. Boxed numbers are: 7, 8
15, 17
18, 20
24, 25
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
ABC is right triangle
AB is longer than side BC, means AB+%3EBC
Boxed numbers are:
7,+8
15,+17
18, 20+
24, 25
If triangle ABC is right triangle, we will use Pythagorean theorem a%5E2+%2B+b%5E2+=+c%5E2.
Before we try out all possible combinations, we can simply use Pythagorean triples and see which ones fit your boxed numbers.
here are first few Pythagorean triples to see where you can find given sides
3,4,5
5,12,13
7,24,25-> this one is your solution
8,15,17-> and this one is your solution
9,40,41+
so, you have
7,24,25 where

AB=c=25
BC=a=24
AC=b=7
check:
24%5E2+%2B+7%5E2+=+25%5E2
576+%2B49+=+625
625+=+625
and 8,15,17->
AB=c=17
BC=a=15
AC=b=8
check:
15%5E2+%2B+8%5E2+=+17%5E2
225+%2B64+=+289
289+=+289