Problem Solving

Hi LUANDATO,

We're told that in triangle XYZ, side XY, which runs PERPENDICULAR to side YZ, measures 24 inches in length and the longest side of the triangle is 26 inches. We're asked for the area, in square inches, of triangle XYZ.

To start, since two of the sides are PERPENDICULAR to one another, they form a right angle (thus, we're dealing with a right triangle). The GMAT has a number of 'Classic' right triangles that it may test you on (including the 45/45/90, 30/60/90, 3/4/5 and 5/12/13). Notice how 26 (the LONG side) is exactly DOUBLE 13 and 24 is exactly DOUBLE 12... this is a 5/12/13 that has been DOUBLED.

Thus, the two 'legs' of the triangle are 10 and 24 and the area of the triangle is...

A = (1/2)(Base)(Height) = (1/2)(24)(10) = (12)(10) = 120

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:In triangle XYZ, side XY, which runs perpendicular to side YZ, measures 24 inches in length. If the longest side of the triangle is 26 inches, what is the area, in square inches, of triangle XYZ?

A. 100
B. 120
C. 140
D. 150
E. 165

Since XY is perpendicular to YZ, the triangle is a right triangle, and hence we can use the Pythagorean theorem to determine side YZ:

(XY)^2 + (YZ)^2 = (XZ)^2

24^2 + s^2 = 26^2

576 + s^2 = 676

s^2 = 100

s = 10

Since the area of a right triangle is half the product of the two legs, we have:

Area of triangle XYZ = ½(24)(10) = 120

Answer: B