Bunuel wrote:
What is x in the diagram below?
A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7
Kudos for a correct solution.Attachment:
2015-07-02_1254.png
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
, If we use side AC as the base in triangle ABC, not sure why the height is not 3 here but x outside of triangle ABC? As thought x is the height for triangle e.g AEB? Then dotted line CE part will be missing as base if AC/E is use as the base for triangle AEB? Have I missed something here? Thanks Brent