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

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 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  The Lengths of the triangle are therefore: Perimeter=Sum of all the lengths 