Question

Δabc is right angled at b bd is its altitude ad 4 cm and dc 12 cm what is the value of ab in cm )?

Answer 1

Answer:

Step-by-step explanation:

all and is stepwise just the pic is of quite low quality but can be seen

Answer 2

Given : ∠B = 90°

To find : AB

Solution :

∠B = 90°

then

$\angle 1 + \angle 2 = 90^\circ$..(1)

Bd is the perpendicular  to AC

thus

$\angle 1 + \angle DCB = 90^\circ ..(2)\\\\\angle DCB = \angle 2 \\\\\angle BAD = \angle 1$

so ,

$\bigtriangleup BCD\sim \bigtriangleup ABD$

BY (AAA ) criterion

therefore ,

$\frac{BC}{AB}=\frac{CD}{BD }=\frac{BD}{AD}\\\\\text{corresponding side of similar triangle }\\\\\frac{BC}{AB}=\frac{12}{BD }=\frac{BD}{4}\\\\BD^2 = 48\\\\BD =\sqrt{48}$

now , using PGT in triangle ABD

$AB^2 = AD^2 + BD^2\\\\AB^2 =4^2+(\sqrt{48})^2\\\\AB^2 = 16+48\\\\AB^2 =64\\\AB = \sqrt{64}\\\\AB = 8 cm$

hence , The value of AB is 8 cm

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