Let's do this question in a triangle, the longest side is 20 centimeter.
Another side is 15 centimeter.
The area of the triangle is 90 square centimeter.
Find the third side.
All right.
So we have BK's equal to 20 abs, equal to 15, and we need to find the value of AC.
All right.
Pause the video, give it a try, and then let's do it together.
All right.
We're back.
I hope you've given it a try.
Let's do it together.
Let's drop a perpendicular from point A to cite B, C.
All right, this is our height and let this point be OK now we have seen that the area of the triangle
is half.
Based in the height.
Right over here, let's take 20 as the base, if you take 20 as the base, then the height is this length
over here, right?
It's the perpendicular distance from the opposite vertex.
To decide if I was to take a B as the base, then the height would be the perpendicular distance from
point C to side A B, right.
And if I have to take AC as the base, the height would be the perpendicular distance from point B to
side easy.
All right, now let's move on or here we are taking B.C. as the base and the height is the perpendicular
distance from point A, which is the opposite vertex to B.C. And we have marked it as it's now it's
given that the area is equal to 90 square centimeter, therefore half in twenty two is equal to ninety.
So I can cut out two from the numerator and the denominator.
So I get X equal to nine centimeter.
All right.
Now A B or is it right angled triangle.
Right.
You can see that this angle over here is a 90 degree angle because that's how we take the height.
And as per Pythagoras's theorem, we can find that 15 square is equal to eight squared plus or B square,
and we have found that it is equal to nine.
So 15 squared is equal to nine squared plus or B squared.
15 squared is 225.
Nine squared is eighty one.
So 225 minus eighty one gives you one forty four.
Therefore Albe Square is equal to one forty four or B is equal to square root of one forty four which
is equal to twelve.
All right.
But we have found that obese 12, we know BK's 20, therefore C will be twenty minus twelve which is
equal to eight centimetre.
Now let's mark that over here.
We have Oak's eight centimetre now a C or is also a right angle triangle.
Right.
Therefore ASBA Pythagoras's Theorem X squared is equal to.
It's square or a square plus orthey square.
We know it his name and we have found all eight.
Therefore Square is nine square plus eight square.
That's eighty one plus sixty four, which is equal to one forty five.
Therefore X equals the square root of one forty five.
And that's approximately 12.
Right.
Because we know 12 square is equal to one forty four, which is very close to one forty five.
And that is your answer.