Question

If the base of an Isosceles Triangle is of length 2a and the length of the
altitude dropped to the base is h, then the distance from the midpoint of
the base to the side of the triangle is​

Answer 1

Answer:

Side of an isosceles triangle is √a^2+ h^2

Step-by-step explanation:

Midpoint if base means distance half so distance = a

altitude = h

then solving by Pythagoras theorem

then you can find final result.

I think it is helpful for you.

Answer 2

Answer:

ah/√h² + a²

Step-by-step explanation:

we need to calculate the length of DE.

Let AB and BC, the sides of isosceles triangle = b units.

Given, BD = h units, AD = DC = a units.

Now In ΔBDC,

by Pythagoras theorem,

b² = h² + a²

=> b = √h² + a²

So BC = √h² + a²

Now in ΔEDC,

SinC = DE /a

=> DE = a SinC.   -------------- [1]

Now to get value of SinC,

Consider the ΔBCD,

SinC = BD/BC = h/√h² + a²  -------------- [2]

Now substitute value of [2] in [1]

DE = aSinC = a *  h/√h² + a² = ah/√h² + a²