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A tile mosaic in the shape of a right triangle is used as the corner for a rectangular pathway. The hypotenuse of the mosaic is 5ft. One side of the mosaic is twice as long as the other side. What are the lengths of the sides? Round your answers to the nearest tenth.

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calculista

Answer:

The lengths of the sides are 2.2 ft and 4.5 ft

Step-by-step explanation:

Let

a -----> the length of one side of the mosaic

b ----> the length of the other side of the mosaic

c ----> the hypotenuse of the mosaic

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] -----> equation A

we have

[tex]a=2b[/tex] -----> equation B

[tex]c=5\ ft[/tex] -----> equation C

substitute equation B and equation C in equation A and solve for b

[tex]5^{2}=(2b)^{2}+b^{2}[/tex]

[tex]25=5b^{2}[/tex]

[tex]b=\sqrt{5}=2.2\ ft[/tex]

Find the value of a

[tex]a=2b[/tex] ------> [tex]a=2\sqrt{5}=4.5\ ft[/tex]

therefore

The lengths of the sides are 2.2 ft and 4.5 ft

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