Very INTERESTING Geometry Problem

Hello everyone, you are welcome. Today we have a very interesting geometry math problem. It is here we have given a right angle triangle whose perimeter is given that is 182 units and its hypotenuse is given which is 85 units. Our target and our job is to find out the area of this right angle triangle. How can we solve this beautiful geometry math problem? First of all let us suppose this is our triangle ABC. So let us suppose this is point A, this is point B, this is point C. Here we have given this side of this right angle triangle. So let us suppose this side is my B and this side is my C. So in this problem here we have given the perimeter of this closed figure. Now what is what about the perimeter? The perimeter of any closed figure is the sum of its all sides, its all boundaries. So here the perimeter of this triangle is the sum of these three sides which is 182. So therefore from this figure we can write perimeter of triangle. So the perimeter of this triangle will become A plus B plus 85. So this will become since A plus B plus 85 is equal to its perimeter is 182. So let's simplify this one equation. So here we will take this 85 to the right hand side. So this will become A plus B is equal to 182 minus 85. By subtracting these two numbers it gives him about A plus B is equal to it is about 97. Let's suppose this is our equation number first. Looking to this one figure this is a right angle triangle. So here in any right angle triangle we can apply the Pythagoras theorem. So here we will apply the Pythagoras theorem and we will find out the weight of A and B, the base and height. So by Pythagoras theorem hypotenuse square is equal to perpendicular square plus base square. So therefore here we can write by Pythagoras theorem which states that hypotenuse square is equal to perpendicular square plus base square. So in this case our hypotenuse is 85, our perpendicular is A and our base is B. So we substitute these values here. So this will become this is 85 square is equal to this is A square plus this is B square. So this becomes B square. Now let us suppose this is our equation number second. Now here in this step in this step we will use an algebraic identity A plus B whole square identity. So here in this step we will use this one identity A plus B whole square is equal to A square plus B square plus two times AB. So here we have the value of A plus B from equation number one which is 97 and the value of A square plus B square from equation number second which is 85 square. So we substitute these two values here in this equation. So this will become value of A plus B simply 97. So it will become 97 square is equal to it has value 85 square plus two times AB and we will take this 85 square to the left hand side. So the value of two times AB will become that will become 97 square minus 85 square. Now this is algebraic identity A square minus B square. So therefore this right hand side will become two times AB will become this will become 97 plus 85 times 97 minus 85. Let's simplify this right hand side. So two times AB will become here this is 7 plus 5 is 12. So 2 8 plus 9 is 17 plus 1 is 18. This is 182 times 7 minus 5 is 2 9 minus 8 is 1. So this is 12. We will divide both sides by 2. So this equation will become this 2 will be cancelled 2 times 1 is 2 2 times 6 is 12. So this is 182 times 6. So therefore value of A times B will become 6 times 2 is 12. 2 1 will be carried 6 times 8 is 48. 48 plus 1 is 49. So this is 9. 4 is carried 6 times 1 is 6. 6 plus 4 is 10. So here this gives him 1092. So here we will use this value of A times B and we will find out the area of the above right angle triangle. So here we will find out the area of this right angle triangle. So we know that the area of any right angle triangle whose base and height is given is half times the product of its two sides where this side represents the base of this triangle and this side represents the height perpendicular of this triangle. So here we have the value of A times B. So we substitute the value of A times B here. So this area will become this will become half times the value of A times B is simply 1092. Let's simplify these two numbers. 2 times 1 is 2. 2 times 5 is 10. 2 times 4 is 10. 2 times 6 is 12. This gives him 546. So therefore the area of this right angle triangle will become 546 square units. So finally the area of this right angle triangle is it is about 546 square units. That is our final answer and final target. In last don't forget to subscribe my youtube channel for such a more interesting and step-by-step geometry solutions. Thanks for watching.