Question

The longer leg of a right triangle is ten less than three times the shorter leg. The hypotenuse

is 4 more than the shorter leg. Find the length of the shorter leg.​

Answer 1

Step-by-step explanation:

solve from this equation

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Answer 2

Answer:

The length of the shortest side is 4.

Step-by-step explanation:

Let the shortest side be a,

Longer leg should be 3a - 10 ( 10 less than 3 times of a )

Hypotenuse should be a + 4( 4 more than a )

Using Pythagoras theorem,

→ a² + ( 3a - 10 )² = ( a + 4 )²

→ a² + 9a² + 100 - 60a = a² + 16 + 8a

→ 9a² + 100 - 16 - 60a - 8a = 0

→ 9a² + 68a + 84 = 0

→ 9a² - 54a - 14a + 84 = 0

→ 9a( a - 4 ) - 14( a - 4 )

→ ( a - 4 )( 9a - 14 ) = 9

→ a = 4 ( taking natural number )

Hence the length of the shortest side is 4.