Question

Two sides of a triangle are $0.5$ cm and $3$ cm. The third side of the triangle is of integral unit. A median is drawn from the common point of side $0.5$ cm and $3$ cm to the third side. Find the length of the median.

Answer 1

The sum of opposite sides of a $△$le is always greater than 3rd side.

$\therefore BC<AB+AC$

$andAB+BC>AC$

$⟹BC>AC-AB$

$\therefore AC-AB<BC<AB+AC$

$3-0.5<BC<3+0.5implies2.5<BC<3.5$

$As,thelengthofBCisintegralvalue.$

$\therefore BC=3cm$

$\therefore a=3cm,b=3cmandc=0.5cm$

$\therefore lengthofmedianfromvertexA$

$mo=\sqrt{\frac{2b^2+2c^2-a^2}{4}}=\sqrt{\frac{2\times 3^2+2{\left(0.5\right)}^2-3^2}{4}}=1.54cm$