00:01
In the given question we are told that the area of a right angled triangle is equal to the area is given as 40 square centimeter and the perimeter of this triangle is given to be equal to 40 centimeters.
00:19
Now we are told to find the hypotenuse, the length of the hypotenuse of this right angled triangle.
00:27
So let's say the lengths of the sides of this hypotenuse are a, b, and the length of the hypotenuse is c units, where c is the length of the hypotenuse.
00:42
And now we can write the area of a triangle can be found by teaching the product half of the base of the triangle times the height of the triangle.
00:57
So this would be equal to half of a times b.
01:01
So the area of this triangle is 40 square centimeters.
01:05
So now from this equation we can write on multiplying 2 on both sides of this equation, 80, 40 times 2 is 80, half times 2 is 1.
01:16
So we would have 80 is equal to a times b.
01:20
Now in the next thing that we are going to use is the pythagoras theorem.
01:25
And according to the pythagoras theorem or the pythagorean theorem, when we have a triangle of this form, a right angled triangle with length of sides as a and b and the length of the hypotenuse as c, we can write a square plus b square is equal to c square is what the pythagorean theorem says.
01:49
So we can take this pythagoras theorem, that is a squared plus b square equal c square and what we would do is we would use an algebraic property over here that is when we have a plus b whole squared it is equal to a squared plus b squared plus two ab so now what we would use this property for is we would add we would add to this expansion a square plus b square we would add a 2 a b over here and subtract a 2 a b as well and the reason why we are doing this is that we can take this part of the theorem now that is a square plus b square equal to c square is what the theorem says we just added 2ab and subtract it to ab and now we can write a square plus b square plus 2 a b as a plus b whole squared right and and this minus 2ab is equal to c squared.
02:59
And now, besides that, in the question we are told that the perimeter of this triangle is 40 centimeters, right? so perimeter means a plus b plus c and this is what is equal to 40 centimeters.
03:18
And from here we can write, from this equation, we can write a plus b is then equal to 40 minus c so this is the pin this is the substitution for a plus b over here so now what we would have is an equation a plus b whole squared minus 2 a b is equal to c squared and in this expression we are going to substitute a plus b is equal to 4...