Question

The areas of two similar triangles are 144 cm² and 64 cm². If one median of the first triangle is 12 cm, then the length of the corresponding median of the second triangle is

Answer 1

The length of the corresponding median of the second triangle is 9.6 cm.

Given: Areas of two triangles, and median of the first triangle.

To find: Length of the corresponding median of the second triangle.

Step-by-step explanation:

• A line segment traced from a vertex to the middle of the opposite side of the vertex is called a triangle's median. At a point, the triangle's medians are converging. The centroid is the point of concurrency.

• The ratio of the squares of the comparable medians is equal to the ratio of the areas of two similar triangles.

Therefore,

⇒$\frac{144}{64}=\frac{14.4^{2} }{x^{2} }$, where $x$ is the median of the other triangle.

⇒ $x^{2}=\frac{(14.4^{2})\times64 }{144}$

⇒ $x=\sqrt{\frac{144}{100}\times64 }$

⇒ $\frac{12}{10}\times8$

∴ $9.6$ cm