Right triangle ABC has sides with length x, y and z. If triangle ABC has perimeter 17, and x² + y² + z² = 98, then what is the area of triangle ABC? A) 12.75 B) 13.25 C) 14 D) 14.5 E) 15.25 Answer: A Source: www.gmatprepnow.com Difficulty level: 700+

let x^2 + y^2 = z^2 x^2 +y^2 +z^2 = 98 substituting, we get 2. z^2 = 98 or z = 7 the hypotenuse is 7 therefore x +y +7 = 17 or x +y = 10 and x^2 + y^2 = 49 or (x + y)^2 - 2xy = 49 replacing x + y =10, we get 10^2 - 2xy = 49 or 2xy = 51 ir xy/2 = 51/4 or area = 12.75 option A

A useful reminder: anytime you need to solve for some variation of a*b, and you're given one equation that defines a + b and a second that defines a² + b², you can create that a*b term by squaring both sides of the a + b equation. Here's a good example of a question where this can come in handy, should you approach algebraically: https://www.beatthegmat.com/ps-diagonal- ... 81412.html

Brent@GMATPrepNow wrote:Right triangle ABC has sides with length x, y and z. If triangle ABC has perimeter 17, and x² + y² + z² = 98, then what is the area of triangle ABC? A) 12.75 B) 13.25 C) 14 D) 14.5 E) 15.25 Answer: A Source: www.gmatprepnow.com Difficulty level: 700+ Let z = length of hypotenuse Let x and y = lengths of the sides that make up the triangle’s right angle NOTE: since triangle area = (base)(height)/2, we know that the area of triangle ABC = xy/2 Given: x² + y² + z² = 98 The Pythagorean Theorem tells us that x² + y² = z² So, we can write: x² + y² + (x² + y²) = 98 Rewrite: 2(x² + y²) = 98 Or we can write: x² + y² = 49 Since we already know that x² + y² = z², we can conclude that z² = 49, which means z = 7 If the perimeter = 17, we can write: x + y + z = 17 Since z = 7, we can write: x + y + 7 = 17 Simplify to get: x + y = 10 IMPORTANT: If we square both sides of the above equation, some nice things happen. (x + y) ² = 10² Expand: x² + 2xy + y² = 100 Rearrange to get: (x² + y²) + 2xy = 100 Replace x² + y² with 49 to get: 49 + 2xy = 100 Simplify: 2xy = 51 NOTE: Our goal is to determine the value of xy/2 So, take 2xy = 51 and divide both sides by 4 to get: xy/2 = 51/4 = 12.75 Answer: A