Question

the base BC of an isosceles triangle ABC is 21cm and AB+BC =29cm , then altitude from the apex vertex A is

A.50cm
B.100cm
C.25cm
D.75cm​

Answer 1

The altitude from the apex vertex A is 7.85 cm

Step-by-step explanation:

Given

AB + BC = 29

BC = 21

Therefore,

AB = 29 - 21 = 8 cm

Since the triangle is isoceles and sum of any two sides is always greater than the third side

Therefore, the side AB = 21 cm

Now semi perimeter of the triangle

$s=\frac{21+21+8}{2}$

$\implies s=\farc{50}{2}$

$\implies s=25$

By Heron's formula

The area of the triangle

$\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}$

$\implies A=\sqrt{25(25-21)(25-21)(25-8)}$

$\implies A=\sqrt{25\times 4\times 4\times 17}$

$\implies A=20\sqrt{17}$

If the altitude from A on BC is h then

The area of triangle is given by

$A=\frac{1}{2}\times BC\times h$

$\implies 20\sqrt{17}=\frac{1}{2}\times 21\times h$

$\implies h=\frac{2\times 20\sqrt{17}}{21}$

$\implies h=\frac{40\sqrt{17}}{21}$

$\implies h=7.85$ cm

Well, the options do not match, but as far as I know, the approach should be this.

Hope this answer is helpful.

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