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 = √(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 ]