Question

The length of the side of a triangle are 10cm,24cm and 26cm.find the length of perpendicular from the opposite vertex to the side whose length is 26cm

Answer 1

as you can see 10² + 24² = 26²

and hence the triangle is right angled.

and length of the perpendicular to the hypotenuse is given by 24*10/26

reason why: use coordinate geometry

equation of line of hypotenuse is x/24 + y/10 = 1.

and use the perpendicular distance formula of point (0,0) to this line.

the formula is :

if line is given by ax+by+c

then distance is |ax1+by1+c|÷(a²+b²) where x1 , y1 is the point from where the perpendicular is dropped onto the line.

you can also use sine rule