98% FAILED to Solve this Simple Math Problem

Hello everyone, you are welcome. Today we have given a right angle triangle and there is only one side given of this right angle triangle. The two sides are not given. We have to find out the perimeter of this right angle triangle. As we know that the perimeter of any closed figure is the sum of the lengths of its boundaries. So here the perimeter of this right angle triangle is the sum of its three sides. So there is only one side given. We have to find out these two sides. So first of all, let us give one name to these sides. Let us suppose this is our A side, this is our side B and this is our side C. So here B side is given. So we have to find out the value of side A and side C. So we will find out these sides using the Pythagoras theorem which states that the hypotenuse square is equal to base square plus perpendicular square. So we will use the formula of hypotenuse which states that hypotenuse square is equal to base square plus perpendicular square. So here in this case our hypotenuse is C, our base is A and our perpendicular is B. So let's substitute these values here. This will become C square is equal to A square plus here perpendicular is B square. So this will become C square A square. We have given the value of B which is 7. So this will become 7 square. Now we will move this A square to the left hand side. So this will become C square minus A square is equal to 7 square is simply 49. Here this is an algebraic identity in the left hand side. So here this left hand side is in this form, x square minus y square which is equal to x minus y times x plus y. So using this algebraic identity here this left hand side will become, this will become C minus A times C plus A is equal to 49. Now looking to the left hand side here is the product of two factors. So we have to make this number as a product of two factors of 49. So therefore the possible factors of this 49 are 1 times 49 and this product gives him 49. And this can also be written as 49 times 1 which is also 49. And this can also be written as 7 times 7 which is also 49. So here we have three possible pair of factors which gives him 49. Now but look into the left hand side here for any two numbers C and A. C minus A must be less than C plus A means that the number in the left hand side will be smaller than this one number. So here only this pair of numbers suits with this left hand side. These two pair of numbers doesn't match with this left hand side. So now here we'll take this expression equal to 1 and this expression equal to 49. So first we can write this as C minus A times C plus A is equal to we can write 49 as 1 times 49. Here we'll compare and take equal this with 1 and this to 49. So this will become C minus A is equal to 1 and C plus A is equal to 49. Let us add these two numbers to find out the value of any variable. So here this negative and this positive will be cancelled and this will become 2C is equal to 1 plus 49 is simply 50. Now let us divide both sides by 2. So here this 2 and this 2 will be cancelled 2 times 1 is 22 times 25 is 50. So therefore the value of C will become 25. This is the value of C we have to find out the value of A. So for that we will substitute this value of C in this equation number second. So this equation number second implies the equation number second is C plus A is equal to 49. Here our C is 25 plus A is equal to 49 and here we move this to the left hand side. So this become A is equal to 49 minus 25. 49 minus 25 is simply 24. So therefore the value of A will become 24. Now here we write these values here the value of A is 24 and the value of C is 25. So here this A is 24 and this C is 25. Here the perimeter of this right angled triangle will become this perimeter will be the sum of these 3 sides that will be A plus B plus C. Here the value of A is 24, the value of B is 7 and the value of C is 25. Now let us add these 3 numbers. So here 25 plus 29 is simply 49. 49 plus 7 is 56. So therefore the perimeter of this right angled triangle will be 56 units. So that is our required answer. This will be 56 units. And last if you like such a more interesting videos, don't forget to like and subscribe my YouTube channel for more interesting videos. Thanks for watching. Take care.