Sum of the squares of the lengths of the two shorter sides (i.e. perpendicular and base) of the right-angled triangle is equivalent to the square of the length of the larger side (i.e. hypotenuse).
[tex]\implies[/tex] H² = P² + B²
Let's takeanexample forbetter understanding.
Question: Eva Lewis wants to put an underground sprinkler system diagonally in her back yard. The measurements of her yard are 45 feet by 60 feet. How long does the sprinkler system need to be?
Solution: It's given that the measurements of Eva Lewis yard are 45 feet by 60 feet. Let's first mark the yard as A, B, C and D.
So, we have AB = CD = 60 ft, BC = AD = 45 ft and angle A, B, C and D is 90°. Means, it's a right angle triangle. Since we don't know the third side. So, let's assume that as 'x'.
In right angled triangle larger side is considered as the 'hypotenuse.' Hence, the formula that we can use to determine the third side is: H² = P² + B². Where H denotes hypotenuse, P denotes perpendicular and B denotes base.
Answers & Comments
Pythagorean theorem is (in a right triangle) the sum of the squares of the two shorter sides is equal to the square of the longest side
Verified answer
Answer:
Sum of the squares of the lengths of the two shorter sides (i.e. perpendicular and base) of the right-angled triangle is equivalent to the square of the length of the larger side (i.e. hypotenuse).
[tex]\implies[/tex] H² = P² + B²
Let's take an example for better understanding.
Question: Eva Lewis wants to put an underground sprinkler system diagonally in her back yard. The measurements of her yard are 45 feet by 60 feet. How long does the sprinkler system need to be?
Solution: It's given that the measurements of Eva Lewis yard are 45 feet by 60 feet. Let's first mark the yard as A, B, C and D.
So, we have AB = CD = 60 ft, BC = AD = 45 ft and angle A, B, C and D is 90°. Means, it's a right angle triangle. Since we don't know the third side. So, let's assume that as 'x'.
In right angled triangle larger side is considered as the 'hypotenuse.' Hence, the formula that we can use to determine the third side is: H² = P² + B². Where H denotes hypotenuse, P denotes perpendicular and B denotes base.
[tex]\implies[/tex] H² = P² + B²
Substitute the values,
[tex]\implies[/tex] (x)² = (45)² + (60)²
[tex]\implies[/tex] x² = 2025 + 3600
[tex]\implies[/tex] x² = 5625
[tex]\implies[/tex] x = 75
Hence, the required answer is 75 ft.