Answer:
hypotenuse = 10.25 inches
Explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
(9x)² + 10² = (x + 10)² ← expand using FOIL
81x² + 100 = x² + 20x + 100 ( subtract x² from both sides )
80x² + 100 = 20x + 100 ( subtract 100 from both sides )
80x² = 20x ( subtract 20x from both sides )
80x² - 20x = 0 ( divide through by 20 )
4x² - x = 0 ← factor out x from each term on the left side
x(4x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x = 0
4x - 1 = 0 ( add 1 to both sides )
4x = 1 ( divide both sides by 4 )
x =
= 0.25
now, x > 0 , then x = 0.25
substitute x = 0.25 into the expression for the hypotenuse
hypotenuse = x + 10 = 0.25 + 10 = 10.25 inches