MATH SOLVE

9 months ago

Q:
# The longer leg of a right triangle is 4 more than twice the shorter leg. The hypotenuse is 4 less than three times the short leg. What is the value of the hypotenuse?

Accepted Solution

A:

Let the shorter leg = x

shorter leg =x

longer leg = 2x + 4

hypotenuse = 3x - 4

Given that a² + b² = c²

x² + (2x + 4)² = (3x - 4)²

Remove brackets : (a + b)² = a² + 2ab + b²:

x² + 4x² + 16x + 16 = 9x² - 24x + 16

Moved all terms to the left:

x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0

Combine like terms:

-5x² + 40x = 0

Multiply all terms by -1:

5x² - 40x = 0

Take out 5x as common factor:

5x(x - 8) = 0

Apply zero product property:

5x = 0 or x - 8 = 0

Evaluate:

x = 0 or x = 8

Since length cannot be zero, shorter leg = 8

shorter leg = 8

Hypotenuse = 3(8) - 4 = 20

Answer: 20 units

shorter leg =x

longer leg = 2x + 4

hypotenuse = 3x - 4

Given that a² + b² = c²

x² + (2x + 4)² = (3x - 4)²

Remove brackets : (a + b)² = a² + 2ab + b²:

x² + 4x² + 16x + 16 = 9x² - 24x + 16

Moved all terms to the left:

x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0

Combine like terms:

-5x² + 40x = 0

Multiply all terms by -1:

5x² - 40x = 0

Take out 5x as common factor:

5x(x - 8) = 0

Apply zero product property:

5x = 0 or x - 8 = 0

Evaluate:

x = 0 or x = 8

Since length cannot be zero, shorter leg = 8

shorter leg = 8

Hypotenuse = 3(8) - 4 = 20

Answer: 20 units