Problem Solving

BTGmoderatorDC wrote: ↑

Tue Feb 18, 2020 8:51 pm

What is x in the diagram below?

2015-07-02_1254.png

A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

OA C

Source: Manhattan Prep

I added some letters to help guide the solution.



Area of triangle = (1/2)(base)(height)
IMPORTANT CONCEPT: we can use ANY of the three sides as our base.

So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.

If we use side AB as the base, then the base has length 12 and the height is 3
So, area of triangle ABC = (1/2)(12)(3)

If we use side AC as the base, then the base has length 7 and the height is x
So, area of triangle ABC = (1/2)(7)(x)

IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.

So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x]
Divide both sides by 1/2 to get: (12)(3) = (7)(x)
Divide both sides by 7 to get: 36/7 = x

Answer: C

Cheers,
Brent