Use the pythagorean theorem to find the lengths of the sides in the right triangle.

Question

Sides are.

3m, 2m+8, 5m

Answer 1

9m² + (2m + 8)² = 25m²; 12m² - 32m - 64 = 0, 3m² - 8m - 16 = 0; (3m + 4)(m - 4) = 0; m = 4 or m = - 4/3 < 0 we rejecting So, m = 4 and sides are 12, 16 and 20

Answer 2

(5m)² = (3m)² + (2m + 8)²

Can you solve for m and answer?

Answer 3

If the sides are 3m, 2m+8, 5m....

Then it looks like 5m is the hypotenuse, so....

We can plug these sides into the equation:

a² + b² = c²

(3m)² + (2m+8)² = (5m)²

and we can square each term

9m² + 4m² + 32m + 64 = 25m²

and simplify (combine like terms)

13m² + 32m + 64 = 25m²

then

0 = 12m² - 32m - 64

We can solve for m using the Quadratic Formula. The solutions are

m = 48/25 and m = -16/25

Since the sides are 3m, 2m+8, and 5m

If we plug in -16/25 we will end up with negative side lengths (there are no negative side lengths) so we disregard that solution.

Finally, all we do now is plug in the other solution m = 48/25

3m = 144/25

2m+8 = 96/25 + 8 = 296/25

5m = 48/5

These are your side lengths.