In triangle XYZ, side XY, which runs perpendicular to side..

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

In triangle XYZ, side XY, which runs perpendicular to side..

by BTGmoderatorLU » Fri Mar 09, 2018 2:59 pm

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

The OA is B.

I'm confused by this PS question, is it a right triangle? Experts, any suggestion about how to solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Fri Mar 09, 2018 2:59 pm

mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 am; Location: London, UK; Thanked: 2 times; Followed by:4 members; GMAT Score:770

by mbawisdom » Sat Mar 10, 2018 6:29 am

LUANDATO 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

The OA is B.

I'm confused by this PS question, is it a right triangle? Experts, any suggestion about how to solve it? Thanks in advance.

(1) yes the triangle is a right angle: "XY, which runs perpendicular to side YZ"
(2) XZ, the hypotenuse, is 26 --> we know this as the longest side of the triangle is 26, if YZ was 26 then XZ would have to be greater than 26.

a^2 + b^2 = c^2
24^2 + YZ^ = 26^2
YZ^2 = 26^2 - 24^2
YZ^2 = (26-24)(26+4)
YZ^2 = (2)(50) = 100
YZ = 10

Area of the a triangle = (1/2)*base*height = (1/2)*(10)*(24) = 120. Answer is B.

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by [email protected] » Sat Mar 10, 2018 4:23 pm

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 09, 2019 6:02 pm

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 = Â½(24)(10) = 120

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]