The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x - 1) cm. What is x?

A.) 7/6

B.) 4/3

C.) 5/3

D.) 3

E.) 5

A.) 7/6

B.) 4/3

C.) 5/3

D.) 3

E.) 5

**Use the Pythagorean Theorem**

a² + b² = c²{in a right triangle, a and b are the legs, and c is the hypotenuse (across from right angle)}

a² + b² = c²

x² + 4² = (2x - 1)² {substituted legs and hypotenuse into Pythagorean Theorem}

x² + 16 = (2x - 1)(2x - 1) {when squaring a binomial, multiply it by itself}

x² + 16 = 4x² - 4x + 1 {used foil method}

3x² - 4x - 15 = 0 {subtracted x² and 16 from each side}

3x² - 9x + 5x - 15 = 0 {split -4x into -9x and 5x, factoring by grouping}

3x(x - 3) + 5(x - 3) {factored 3x out of first two terms and 5 out of last two terms}

(x - 3)(3x + 5) = 0 {factored (x - 3) out of the two terms}

x - 3 = 0 or 3x + 5 = 0 {set each factor equal to 0}

x = 3 or 3x = -5 {added 3 and subtracted 5}

x = 3 or x = -5/3 {divided second equation by 3}

x is a leg of a triangle and cannot be negative

x = 3

**D.) 3**

**Ask Algebra House**