Question 11. Page 60. Triangles & Diagonals Problem Set.

[karthiksms]

This question comes from Manhattan Guide in Geometry.

Could someone please explain?

I understand that area is 18 is we take 12 as the base of the bolded triangle.

Not sure why we would say that 1/2*7*x is 18 ?

For 1/2*7*x, where is 7 coming from? 7 is the length only for the bolded line, what about the length for the dotted line after that if we consider 7 as the base? And how is it possible to make that result equal to 18?

[tommywallach]

Hey Karthik,

Any side of a triangle can be seen as the base, as long as you reorient. In the picture here, if 12 is the base, then the height is 3. If 7 is the base, then the height is x.

Remember, the height of a triangle is defined as: "The line that reaches from the highest point of the triangle and meets the base or an extension of the base at a 90 degree angle." So the line x is the height when 7 is the base, because it meets the extension of the base (where the right angle has been drawn in).

So, we already know the area is 18 from the work we did before:

1/2 * b * h = area = 1/2 * 12 * 3 = 18

At this point, we can get to x by using the same formula:

1/2 * b * h = 18

so

1/2 * 7 * x = 18

Remember, we already worked out why x is the height when 7 is the base, but we're still solving for the exact same triangle!

So x = 36/7

Hope that helps!

-t