The length of one leg of a right triangle is three times as large as the length of the other leg. If the hypotenuse has a length of 10 inche

Question

The length of one leg of a right triangle is three times as large as the length of the other leg. If the hypotenuse has a length of 10 inches, which of the following is the perimeter of the triangle in inches? squareroot 10 4 squareroot 10 10 10 + squareroot 10 10 + 4 squareroot 10 Solution:The correct answer is E. If the length of the smaller leg is x then the larger leg is 3x, and by the Pythagorean Theorem, the hypotenuse is squareroot x^2 + 9x^2 = squareroot 10 x^2 = x squareroot 10 = 10, the given length. Solving for x, x 10/squareroot 10 = 10 squareroot 10/10 = squareroot 10, and the perimeter is squareroot 10 + 3 squareroot 10 + 10.

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Natalia 4 days 2021-10-10T05:06:25+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T05:07:41+00:00

    Answer:

    Perimeter == 10 + 4√10

    Step-by-step explanation:

    Let the length of the smaller leg be x and thus since the bigger leg is 3 times the size of the smaller one, the bigger leg is 3x.

    Now, from the question we are given that the hypotenuse is 10 inches.

    Now since this is a right angle triangle, let’s use Pythagoras theorem to which says;

    a² + b² = c²

    Where c is the hypotenuse, while a and b are the other sides of the triangle.

    Thus, fixing x and 3x for a and b respectively and 10 for c, we have;

    x² + (3x)² = 10²

    So, x² + 9x² = 100

    Thus, 10x² = 100

    Divide both sides by 10 to get,

    x² = 10

    Take square root of both sides to get ; x = √10

    Thus since one side is x and the other 3x,thus the dimensions of the triangle are √10, 3√10 and 10.

    Now, perimeter of triangle is the sum of all 3 sides.

    Thus perimeter = (√10) + 3(√10) + 10

    = 10 + 4√10

    0
    2021-10-10T05:07:52+00:00

    Answer:

    Perimeter=(10+4\sqrt{10}) inches

    Step-by-step explanation:

    Let the length of one leg of the right angle triangle=x

    The length of the other leg is three times as large as the length of the other leg = 3x

    The Length of the hypotenuse=10 inches

    From Pythagoras theorem

    Hypotenuse^2=Opposite^2+Adjacent^2

    10^2=x^2+(3x)^2\\100=x^2+9x^2\\100=10x^2\\x^2=100/10=10\\x=\sqrt{10}

    The Lengths of the triangle are therefore: \sqrt{10} ,3\sqrt{10} and 10 inches

    Perimeter=Sum of all the lengths

    =\sqrt{10} +3\sqrt{10} + 10 inches\\=(10+4\sqrt{10}) inches

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