abc is a triangle right angled at B If AB 5cm and BC 10cm then what is the length of the perpen...........

Quantitative Aptitude (CDS) Mensuration 2D

abc is a triangle right angled at B. If AB=5cm and BC=10cm, then what is the length of the perpendicular drawn from the vertex B to the hypotenuse?

4 cm

2 $\sqrt{5}$ cm

$\frac{4}{\sqrt{5}}\; cm$

8 cm

Hypotenuse AC² = 10² +5²

AC² = 100+25 = 125

AC = 5√5

Area = (1/2) * base *height

Area = (1/2)*AB*AC

Area = (1/2) *5*10 = 25

Area can also be written as

Area =(1/2)*AC*BD =(1/2)*5√5*BD = 25

BD =25*2/(5√5) = 2√5 cm

Length of the perpendicular drawn from the vertex B to the hypotenuse = 2√5 cm

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