Answer:
legs are 21 cm and 20 cm
Explanation:
let x be the length of 1 leg then the other leg is x - 1
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 legs, then
x² + (x - 1)² = 29² ← expand factor on left side using FOIL
x² + x² - 2x + 1 = 841
2x² - 2x + 1 = 841 ( subtract 841 from both sides )
2x² - 2x - 840 = 0 ( divide through by 2 )
x² - x - 420 = 0 ← in standard form
(x - 21)(x + 20) = 0 ← in factored form
equate each factor to zero and solve for x
x - 21 = 0 ⇒ x = 21
x + 20 = 0 ⇒ x = - 20
However , x > 0 , then x = 21 and x - 1 = 21 - 1 = 20
length of legs are then 21 cm and 20 cm