The triangle shown has an area of 45.5 square inches. Find the measure of the height (segment LM).

  7 inches

Step-by-step explanation:

The area is given by the formula ...

  A = (1/2)bh

Filling in the given values, we can solve for h.

  45.5 = (1/2)(13)h

  45.5/6.5 = h = 7

The height of the triangle is 7 inches.

Comment on the geometry

If you work the problem by computing the length of KM, then the length of LM, you will get a different answer. The area of the triangle shown is actually about 46.76 square inches. In other words, the numbers describing this geometry are inconsistent, so will give inconsistent answers if you work the problem different ways.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225