Question

The sides of a right triangle are 9 cm, 12 cm, and 15 cm long. Then the sum of the square of the medians is equal to

• A. 332.5 cm
• B. 335.5 cm
• C. 337.5 cm
• D. 339.5 cm

Answer 1

The correct option is C 337.5 cm

Using apollonies theorem

$3(A{B}^2+B{C}^2+A{C}^2)=4(A{D}^2+B{E}^2+C{F}^2)$

$AB=9cm$, $BC=12cm$, $CA=15cm$

AD, BE, CF are medians

$\Rightarrow A{D}^2+B{E}^2+C{F}^2=\frac{3}{4}(A{B}^2+B{C}^2+A{C}^2)$

$=\frac{3}{4}\left[\right(19{)}^2+(12{)}^2+(15{)}^2]$

$=\frac{3}{4}[81+144+225]$

$=\frac{3}{4}\times 450$

$=337.5$cm.