# The legs of a right-angled triangle are 6: 8, and its hypotenuse is 1 dm. Find the perimeter of the triangle.

July 29, 2021 | education

| Let the length of the first leg be 6x dm, and the second 8x dm. Then we can write an expression for finding the hypotenuse according to the Pythagorean theorem:

1 = 6x ^ 2 + 8x ^ 2;

Let’s simplify the expression:

1 = 100x ^ 2.

Let’s take the square root of the left and right sides of the equation:

1 = 10x

From here we find x:

x = 1:10;

x = 0.1 dm.

Hence, the first leg is equal to:

0.1 * 6 = 0.6 dm

And second:

0.1 * 8 = 0.8 dm

Now we can find the perimeter of the triangle – add the lengths of the legs and the hypotenuse:

0.6 + 0.8 + 1 = 2.4 dm.

Answer: The perimeter of the triangle is 2.4 dm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.