The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the

Question

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible
lengths of the third side of the triangle? Round your answer to the nearest tenth.
O
O
O
O
3.1 inches
3.2 inches
10.0 inches
15.7 inches

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Katherine 2 weeks 2021-09-11T00:29:13+00:00 2 Answers 0

Answers ( )

  1. Answer:

    B) 3.2 inches

    Step-by-step explanation:

    did it on edge

    0
    2021-09-11T00:31:06+00:00

    Answer:

    The difference between the two possible  lengths of the third side of the triangle is:

                                3.2 inches

    Step-by-step explanation:

    The lengths of two sides of a right triangle are 5 inches and 8 inches.

    This means that the third side could be the hypotenuse of the triangle or it could be a leg of a triangle with hypotenuse as: 8 inches.

    Let the third side be denoted by c.

    • If the third side is the hypotenuse of the triangle.

    Then by using the Pythagorean Theorem we have:

    c^2=5^2+8^2\\\\i.e.\\\\c^2=25+64\\\\i.e.\\\\c^2=89\\\\i.e.\\\\c=9.434\ inches

    • and if the third side i.e. c is one  of the leg of the triangle with hypotenuse 8 inches then the again by using Pythagorean Theorem we have:

    8^2=c^2+5^2\\\\i.e.\\\\64=c^2+25\\\\i.e.\\\\c^2=64-25\\\\i.e.\\\\c^2=39\\\\i.e.\\\\c=\sqrt{39}\\\\i.e.\\\\c=6.245\ inches

    Hence, the difference between the two possible lengths of the third side is:

    =9.434-6.245\\\\=3.189\ inches

    which to the nearest tenth is: 3.2 inches

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