Math, asked by Kjw, 8 months ago

Equal sides of an isosceles triangle are 13 cm each and the Base is 10 cm. find the altitude from the vertex to the Base of the triangle

Answers

Answered by pragati229
1

Step-by-step explanation:

1) Given :

ABC be an isosceles triangle whose congruent sides are AC and BC.

AC=BC=13cm

AB = 10cm.

2) We will mark all points by taking origin as A (0,0) in first Quadrant of Cartesian Co-ordinate system.

Then,

A= (0,0)

B = (10,0)

Now,

I isosceles triangle,

CE is median passing through centroid D

Therefore,

AE = BE = 5cm

=> E = (5,0)

3) In triangle ACE,

By Pythagoras Theorem,

EC^2. = AC^2 - AE^2

=> EC^2 = 13^2 - 5^2

=> EC = 12cm

=> C = (5,12)

4) Centroid of triangle ABC,

C =( ( x1 + x2 + x3)/ 3 ,(y1+y2+y3)/3 )

=> C =((0+ 10+ 5)/3 ,(0+0+12)/3

=> C = (15/3 , 12/3 )

=> C = (5, 4)

5) Required :

By distance formula,

Distance between vertex opposite the base and controid is :

CD =

\begin{gathered}cd = \sqrt{ {(5 - 5)}^{2} + {(12 - 4)}^{2} } \\ = > cd \: = 8cm\end{gathered}cd=(5−5)2+(12−4)2=>cd=8cm

Hence,

Distance between the vertex opposite the base and the controid is 8cm.

NOW PLESS MARK ME BRAINIEST

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