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
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)} 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 Comments are closed.

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