Question

Find the length of hypotenuse of a right angled triangle ABC with angle ABC =90° and AB=BC =a

Answer 1

Given,
AB = BC= (a) units.
By using Pythagoras theorem,
$\: \: \: \: \: \: \: \: \: AC = \sqrt{ {AB }^{2} + {BC}^{2} } \\ = > AC = \sqrt{ {a}^{2} + {a}^{2} } = \sqrt{2 {a}^{2} } \\ = > AC = a \sqrt{2}units.$



Hope this will help you. 

If you like my answer
Please mark it as brainliest 
And 
Be my follower if possible.

Answer 2

SOLUTION......



AB = BC = a

Let, length of the Hypotenuse[AC] be x.

It is given that Angle ABC is 90° or right angle. So, Triangle ABC is an Right Angled Triangle at angle B.

So, we use Pythagoras Theoram in Triangle ABC.

[ ▪ Pythagoras Theoram :- If a triangle is right angled triangle, then the square of the hypotenuse is equal to the sum of sauares of other two sides of a triangle. ]

So,
In Triangle ABC,

According To Pythagoras Theoram -

AC^2 = AB ^2 + BC ^2
${x}^{2} = {a}^{2} + {a}^{2} \\ \\ {x}^{2} = 2 {a}^{2} \\ \\ x = \sqrt{2 {a}^{2} } \\ \\ x = a \sqrt{2} ...........is \: the \: required \: answer \: of \: your \: question. \\ \\ \\ \\ hope \: this \: will \: help \: you..... \\ \\ \\ have \: u \: any \: doubt \: then \: ask \: me..$