The legs of a right triangle have lengths of 28 meters and 21 meters. the hypotenuse has a length of 5x meters. what is the value of x?

We have a right triangle with

a = one leg = 28

b = other leg = 21

c = hypotenuse = 5x

use the pythagorean theorem (a^2+b^2 = c^2) and solve for x

a^2+b^2 = c^2

28^2+21^2 = (5x) ^2

784+441 = 25x^2

1225 = 25x^2

25x^2 = 1225

(25x^2) / 25 = 1225/25

x^2 = 49

sqrt (x^2) = sqrt (49)

|x| = 7

x = 7 or x = - 7

Since the hypotenuse has length 5x meters, this means

5x = 5*7 = 35

or

5x = 5 (-7) = - 35

Toss out the negative length as it makes no sense.

The only value of x is x = 7

Therefore the final answer is x = 7