Question

What is the height??

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Here, we have given

• One isosceles triangle that means the given triangle having two sides equal.
• The dimensions of the triangle are 21cm, 21 cm and 16 cm.

Consider the given triangle as ABC . In ΔABC, AD acts as a median. It means Angle ADB = 90°

Therefore,

By using Pythagoras theorem,

• It states that the sum of the squares of base and perpendicular height is equal to the square of the hypotenuse.

That is,

$\bold{ ( Hypotenuse) ^{2} = (Perpendicular) ^{2} + (base) ^{2}}$

Subsitute the required values

$\sf{ AC^{2} = AB^{2} + BC^{2}}$

$\sf{ (21)^{2} = (h) ^{2} + (16)^{2}}$

$\sf{ 441 = (h)^{2} + 256}$

$\sf{ (h)^{2} = 441 - 256}$

$\sf{ h^{2} = 185}$

$\sf{ h = \sqrt{185}}$

$\bold{ h = 13.6 \: cm}$

Hence, The required height of the given isosceles triangle is 13.6 cm.

[ Note :- you can also solve this problem by using Heron's Formula but it's too lengthy to solve that's why I have used simple method ]