Question

in the given figure abc angle abc=90° BD is perpendicular to AC if ab=6cm, BC=8 cm CA= 10 cm then the length of the ad is
a)6.3 cm
b)3.6 cm
c)3 cm
d)4 cm
please answer the question with explanation​

Answer 1

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Answer 2

Concept

Pythagoras theorem says that in a right angled triangle the square of hypotenuse is equal to sum of squares of base and perpendicular of that right angled triangle.

Given

AC=6cm, BC=8 cm, CA=10 cm and angle BDC is 90°.

To find

The length of AD.

Explanation

Let AD=x, DC=10-x.

In triangle DBC.

AD is perpendicular.

BC is hypotenuse.

DC is base.

It is a right angled triangle and we have to use pythagoras theorem.

$BC^{2} =DC^{2}+ DB^{2}$

DB=$\sqrt{BC^{2} -DC^{2} }$

DB=$\sqrt{64-(10-x)^{2} }$--------------1

In triangle ADC.

DB is perpendicular.

AB is hypotenuse.

AD is base.

It is a right angled triangle and we have to use pythagoras theorem.

DB=$\sqrt{36-x^{2} }$-----------------------2

Equating 1 and 2.

$\sqrt{64-(10-x)^{2} }$=$\sqrt{36-x^{2} }$

Squaring both sides.

64-($100+x^{2} -20x$)=36-$x^{2}$

64-100-$x^{2}$+20x=36-$x^{2}$

-36+20x=36

20x=36+36

20x=72

x=72/36

x=3.6 cm

Hence the length of AD is 3.6cm.

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