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The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg:Length of the longer leg:Length of the hypotenuse:

User Christal
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Let l be the length of the longer leg, s be the length of the shorter leg, and h be the length of the hypotenuse, then we can set the following equations:


\begin{gathered} l=s+7cm\text{.} \\ h=s+9\operatorname{cm}\text{.} \end{gathered}

Using the Pythagorean theorem we get:


h^2=l^2+s^2.^{}

Substituting the first and second equation in the above one we get:


(s+9cm)^2=(s+7\operatorname{cm})^2+s^2\text{.}

Solving for s we get:


\begin{gathered} s^2+s\cdot18\operatorname{cm}+81\operatorname{cm}=s^2+s\cdot14\operatorname{cm}+49\operatorname{cm}^2+s^2, \\ s\cdot18\operatorname{cm}+81\operatorname{cm}^2=s^2+s\cdot14\operatorname{cm}+49\operatorname{cm}^2, \\ s^2-s\cdot4\operatorname{cm}-32\operatorname{cm}^2=0, \\ (s-8\operatorname{cm})(s+4\operatorname{cm})=0, \\ s=8\operatorname{cm}. \end{gathered}

Substituting s=8cm in the first and second equation we get:


\begin{gathered} l=8\operatorname{cm}+7\operatorname{cm}=15\operatorname{cm}, \\ h=8\operatorname{cm}+9\operatorname{cm}=17\operatorname{cm}\text{.} \end{gathered}

Answer:

Length of the shorter leg: 8cm.

Length of the longer leg: 15cm.

Length of the hypotenuse: 17cm.

User Raviabhiram
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