Question

In triangle abc angle b =90 AB:BD:DC=3:1:3 IF AC=20cm what is ad

Answer 1

Answer:

Step-by-step explanation:

Answer 2

AD=12.6 cm

Step-by-step explanation:

AB:BD:DC=3:1:3

Let AB=3x, BD=x,DC=3x

BC=BD+DC=x+3x=4x

Angle B=90 degrees

AC=20 cm

In right triangle ABC

$AC^2=AB^2+BC^2$

Using Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

Substitute the values then we get

$(20)^2=(3x)^2+(4x)^2$

$400=9x^2+16x^2$

$400=25x^2$

$x^2=\frac{400}{25}=16$

$x=\sqrt{16}=4$

AB=3(4)=12 cm

BD=4 cm,DC=3(4)=16cm

In triangle ABD

$AD^2=AB^2+BD^2$

$AD^2=(12)^2+4^2=144+16=160$

$AD=\sqrt{160}=12.6 cm$

Hence, AD=12.6 cm

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