Question

In triangle LMN , medians MX and NY are perpendicular to each other and intersect at Z. If MX= 8cm , NY = 12cm , what is the area of triangle LMN?

Answer 1

Given: Medians MX and NY are perpendicular to each other, intersects at Z, MX= 8cm , NY = 12cm.

To find:  The area of triangle LMN?

Solution:

• Now from the triangle we can understand that Z is the centroid of the triangle LMN.

• So, since Z is the centroid, we get:

          NZ = 2YZ

          8/2 = YZ

          YZ = 4 cm

• So, area ∆NMX = 1/2 * 8 * 8 = 32cm².

• So now as we know that the median divides the triangle into two equal areas, so:

                   area ∆LMN =  area ∆NMX x 2

                   = 2 x 32 cm²

                   = 64 cm²

Answer:

        So, the area of triangle LMN is 64 cm².