Question

Find the value of x in a triangle . If the hypotenuse of the triangle is 10 , the opposite is x+2 and the adjacent is x.​

Answer 1

Answer:

x = 6

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

however, x > 0 , then x = 6