Math CentralQuandaries & Queries


Question from Lorena, a parent:

A wire 24 dm is bent to form a right triangle. The ratio of the shorter leg to the hypotenuse is 3:5. Find the length of the longer leg?

Hi Lorena,

Suppose the length of the short leg is $a$ dm, the length of the longer leg is $b$ dm and the length of the hypotenuse is $h$ dm. You know three facts

  1. $a + b + h = 24$

  2. $\frac35 = \frac{a}{h}$ and

  3. $a^2 + b^2 = h^2$.

Solve these equations for $b.$


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