Final answer:
Using the Pythagorean theorem, the length of the hypotenuse is calculated to be 35 m. However, this does not match any of the multiple-choice options provided for the value of x, which should be 7. This indicates a potential error in the question or its choices.
Step-by-step explanation:
The question involves applying the Pythagorean theorem to a right triangle where the legs have lengths of 28 m and 21 m, and the hypotenuse is given as 5x meters. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²). To find x, we must first calculate the hypotenuse using the known leg lengths and then solve for x.
First, we find the hypotenuse:
c = √(28² + 21²) = √(784 + 441) = √1225
Since √1225 = 35, we have 5x = 35. To solve for x:
x = 35 / 5 = 7
However, given the options a. 3, b. 4, c. 5, d. 6, none of them match the calculated value of x which is 7. Therefore, either there is a typo in the question or choices, or there is a misinterpretation of the question.