SOLUTION: For a pair of similar figures, find the length of 2 unknown sides (that is, those two sides whose lengths involve the variable x). There is a large triangle with 5x on the left

Algebra ->  Pythagorean-theorem -> SOLUTION: For a pair of similar figures, find the length of 2 unknown sides (that is, those two sides whose lengths involve the variable x). There is a large triangle with 5x on the left       Log On


   

Question 130927: For a pair of similar figures, find the length of 2 unknown sides (that is, those two sides whose lengths involve the variable x).
There is a large triangle with 5x on the left side (straight, long side) and 4 on the bottom.
There is a small triangle with 5 on the left side (straight, long side) and x on the bottom.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
"In similar triangles, corresponding sides are proportional"
From the problem description, you can write:
5x%2F5+=+4%2Fx "The ratio of the long side (5x) of the first triangle to the long side (5) of the second triangle is equal to the ratio of the base of the first triangle (4) to the base (x) of the second triangle".
Solve the above proportion for x.
5x%2F5+=+4%2Fx Cross-multiply.
5x%5E2+=+20 Divide both sides by 5.
x%5E2+=+4 Take the square root of both sides (use only the positive answer).
x+=+2
The lengths of the two unknown sides are:
5x+=+5%282%29 = 10 and...
x+=+2