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the hypotenuse of a right triangle measures 29 cm. one leg is 1 cm shorter than the other. what are the lengths of thelegs?

User ConFusl
by
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1 Answer

4 votes

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

User Joselo
by
9.1k points
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