SOLUTION: suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.

Algebra ->  Pythagorean-theorem -> SOLUTION: suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.       Log On


   

Question 205537: suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.
draw a picture and label all the sides.

(i cant seem to figure out how to label all sides?)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
problem:
suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.
draw a picture and label all the sides.
-----
your picture can be found at the following website:
http://theo.x10hosting.com/
-----
look for 205537 and click on it.
if it's not there, wait about 30 minutes and try again.
it will be there.
-----
points of triangle are ABC.
-----
line AC is called side b (opposite angle B)
line BC is called side a (opposite angle A)
line AB is called side c (opposite angle C)
-----
angle C is 90 degrees making it the right angle of the triangle
-----
c is the longest side of the triangle because it is the hypotenuse.
a is the shortest side of the triangle because we made it that way.
b is the third side of the triangle.
-----
problem states that the shortest side is 8 feet less than the longest side.
that means that a = c - 8
-----
the problem also states that the third side is 7 feet more than the shortest side.
that means that b = a + 7
-----
we let c = x because we don't know how long it is and we allow x to represent the length of it.
-----
if a = c - 8 and c = x then a = x - 8
if b = a + 7 and a = x - 8 then b = (x - 8) + 7 = x - 1
-----
now we have:
a = x-8
b = x-1
c = x
-----
you can solve for x by using the pythagorean formula.
the pythagorean formula states that:
c%5E2+=+a%5E2+%2B+b%5E2 where c is the hypotenuse of the triangle.
we constructed the triangle so that side c would be the hypotenuse so the picture and the formula should be synchronized.
-----
my answer is:
c = 13
b = 12
a = 5
-----
you can see that a is the shortest side and is 8 less than c which is the longest side.
you can see that b is the third side and is 7 more than a which is the shortest side.
-----
if you solve it you should get the same answer.