BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:50 pm

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

Answer: D

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

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:50 pm

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

Answer: D
Source: Veritas Prep

Scott's solution is pretty much 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