GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
In the above diagram, what is the value of x?
NOTE: Enter your answer as a
fractionI 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: 36/7
Cheers,
Brent
Hey Brent.
I used properties of similar triangles to solve this question, and was wondering if that method is correct given your explanation using the area instead.
Using your labelled diagram, proving that triangle ADC is similar to triangle AEB went like this:
\(=>\) Triangle AEB has a right angle, and so does Triangle ADC
\(=>\) Triangle AEB and Triangle ADC share angle EAB
\(=>\) Since two of their angles are the same, their third angle must also be the same
\(=>\) Therefore, they are similar triangles
So it follows that:
\(\frac{7}{3} = \frac{12}{x}\)
\(7x = 36\)
\(x = \frac{36}{7}\)