Question

If QP=25, MN=35, and SR=13, calculate the area of triangle LMN.
A. 568.8 units
B. 227.5 units
C. 437.5 units
D. 796.3 units

Answer 1

any idea? @wolf1728 My geometry is absolutely pathetic.

Answer 2

Let's see how we can do this in the simplest form. Realise that the area of a triangle is (B * H) / 2, where B is already given: B = MN = 35 units.

H is the distance LR, which is only partially known (LR = LS + SR, with SR = 13. We need to establish LS in order to find LR and thus H.

Notice that the difference between MN and QP is 10 (35 - 25). So for every decrease of 10 units on a line parallel to MN or QP, you have to move this line 13 units up. Example: for MN = 35 to decrease to QP = 25, Qo has moved 13 units up to the top of the triangle.

If we would move line QP upward with another 13 units, we would then expect this new line to be 25 - 10 units = 15 units long. So for every 10 units to be knocked off the length, the line shifts upward with 13 units. This means that a 25 unit line will reduce to 0 lengt (at the top) after (25/10) * 13 units = 2.5 * 13 units = 32.5 units. This is the length of LS.

The total height H is now H = LR = LS + SR = 32.5 + 13 = 45.5 units. The area of the triangle will then be (H * B) / 2 = (45.5 * 35) / 2 = 796.25 == 796.3 units