The sides of right triangle ABC are such that the length of

Question

The sides of right triangle ABC are such that the length of side AB is greater than the length of side BC, which itself is greater than the length of side AC. If side AB = 143 and side AC = 55, what is the area of the triangle?

A. 3113
B. 3224
C. 3432
D. 3630
E. 7260

A. 3113
B. 3224
C. 3432
D. 3630
E. 7260

Bunuel · Answer

Given that AB>BC>AC. So, AB is the hypotenuse of the triangle.

BC=\sqrt{143^2-55^2}=\sqrt{(11*13)^2-(11*5)^2}=11\sqrt{13^2-5^2}=11*12 .

The area = 1/2*BC*AC = 1/2*(11*12)*55 = 66*55 = 3630.

Answer D.

BrentGMATPrepNow · Answer

Bunuel's solution is exactly how I would have answered this question. 
However, if I had no idea how to answer the question (or if I had only 10 seconds remaining), I still would have guessed D.

Here's why: 
Notice that E (7260) is twice as big as D (3630).
Since area of a triangle = ONE-HALF times base times height, answer choice E is a good distractor for people who forget to HALVE the product of the base and height. 
So, I'd GUESS D.

Cheers,
Brent

shasadou · Answer

There is a special property for a right triangle which is valid here 5k:12k:13k

UttamGiet · Answer

According to right angle property: sides ratio 5x:12x:13x

Here AC>BC>AB
13>12>5

Here AC =143= 13*11 so X=11 BC=12*11

Area= .5*AB*BC
= .5*55*12*11=3630

ScottTargetTestPrep · Answer

Solution:

Since we are given that triangle ABC is a right triangle and AB is the longest side, so AB must be the hypotenuse of the triangle. Using the Pythagorean theorem, we have:

(AC)^2 + (BC)^2 = (AB)^2

55^2 + x^2 = 143^2

x^2 = 143^2 - 55^2

Noting that the right side of the equation is a difference of two perfect squares, we have:

x^2 = (143 + 55)(143 - 55)

x^2 = (198)(88)

x^2 = 2 * 99 * 8 * 11

x^2 = 16 * 9 * 11 * 11

x = √(16 * 9 * 11^2) = 4 * 3 * 11 = 132 = length of side BC

Since the area of a right triangle is half the product of the lengths of its two legs, the area of triangle ABC is ½ * AC * BC = ½ * 55 * 132 = 66 * 55 = 3630.

Answer: D

Karan911 · Answer

Hi,

So it took me a long while to get the right triangle idea, I went down the idea of 'third side < sum of the other 2 sides and gr8r than diff of other 2,so if you do so:

143-55 < BC < 143+55
88 < BC < 198,
but we're given that BC is smaller than 143,
so 88 < BC < 143

Now ideally we'll need BC to find the area (they're not gonna give us 2 sides as base and height ever lol]
So since AB is the greatest, I considered AC perpendicular to BC.

Now1/2*AC*BC, will give me 1/2*55 * (something) since all and choices are integers, the 'something' has to be even, and hence unit digits zero, so only last 2 options left.

Bunuel  is there any possible flaw here?

Max BC can be is 142 which would mean 142/2 is something higher than 70, so into 55 is definitely not gonna be 7000 something, so answer E is out.

Option D is correct

The sides of right triangle ABC are such that the length of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The sides of right triangle ABC are such that the length of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards