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A printer creates a right triangular card where the hypotenuse, h, is three times as long as the shorter leg. What is the length of the longer leg, l, in terms of h? Write the answer in simplest form by replacing a, b, and c with the correct values.

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semsee45

Answer:

[tex]l=\frac{2\sqrt{2} }{3}h [/tex]

Step-by-step explanation:

[tex]a^2+b^2=c^2[/tex]

[tex](\frac{h}{3})^2+l^2=h^2 [/tex]

[tex]l^2=h^2-(\frac{h}{3})^2\\[/tex]

[tex]l^2=h^2-\frac{h^2}{9}[/tex]

[tex]l^2=\frac{8}{9}h^2[/tex]

[tex]l=\sqrt{\frac{8}{9} h^2} =\frac{2\sqrt{2} }{3}h [/tex]

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