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
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.
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