If / 61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang

answer in simplest radical form.

A. 5

B. 6

C. 2V15

D. 6V10

A. 5

Step-by-step explanation:

The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.

From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:

(√61) ² = (x) ² + (x + 1) ²

x² + x² + 2x + 1 = 61

2x² + 2x + 1 - 61 = 0

2x² + 2x - 60 = 0

Dividing through by 2 gives:

x² + x - 30 = 0

x² + 6x - 5x - 30 = 0

x (x + 6) - 5 (x + 6) = 0

(x-5) (x+6) = 0

x-5 = 0 or x+6 = 0

x = 5 or x = - 6

Since the length of a side cannot be negative, x = 5 units