A triangle has sides of 4, 7, and 10.

Question

In a similar triangle the shortest side is 12 and the longest is x. 

(a) Write a proportion that models the situation.

(b) Solve the proportion for x.

( The proportion is ? Type an equation. Do not simplify.)

Answer 1

 

Let's name each side of triangle 1:  A = 4, B = 7, and C = 10

The shortest side in a similar triangle is 12, so that would be the same side as A in triangle 1 and the longest is x which is the same side as C in triangle 1.

Therefore, our proportion statement is 4 is to 10 as 12 is to x, or

      4       12

    ___ = ____    which is the answer to a

      10      x

 

To solve for x, we cross multiply and we get

    4x = (10)(20) or      4x = 120

Divide both side of the equation by 4 to isolate x:  x = 120/4, so x = 30 (the answer to b)