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.

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

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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

no

step-by-step explanation: