|
Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: buffalo on Sep 3, 2012 one leg of a right triangle is length 20. the lengths of the other leg and the hypotenuse are conseutive odd integers. compute the length of the hypotenuse
how is it 101 explain and show steps how to get ansewr what is conseutive odd integers, like conseutive is 1,2,3,4, meaning the idffrence is 1, so isthe differnce 1 for conseutive odd or even Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: buffyjo29 on Sep 3, 2012 n = other leg
n + 2 = hypotenuse (consecutive odd integer) 20^2 + n^2 = (n+2)^2 and solve for n. When we say consecutive odd integers, we mean only from the odd integers, like 41, 43, 45, 47 are consecutive. The even integers in-between aren't counted. Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: julies on Sep 3, 2012 Let the length of the unknown leg be
2x-1, then the hypotenuse is 2x+1. & 400+(2x-1)^2=(2x+1)^2=> 8x=400=> x=50 So, the length of the hypotenus is 2(50)+1=101 Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: buffet55 on Sep 3, 2012 First, the odd integers are... 1,3,5,7,9 etc...
Examples of consecutive odd integers would be 5 and 7, 21 and 23, 99 and 101 etc... You can define them as... x and x + 2 So using the Pythagorean Theorem... 20^2 + x^2 = (x + 2)^2 You know that the hypotenuse is x + 2 since the hypotenuse must be the longest side So... Multiply out the square... 400 + x^2 = x^2 + 4x + 4 Subtract x^2 from each side... 400 = 4x + 4 Divide each side by 4... 100 = x + 1 Subtract 1 from each side... 99 = x The first leg was defined as 20 The second leg is x or 99 The hypotenuse is x + 1 or 101 Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: dave67tapout on Sep 3, 2012 Jenny,
A small favor: next time you post, use a spell checker. Now, consecutive odd integers are 1,3,5,7,...They differ by 2, not 1. An odd number can be written as 2n+1 where n is any number. How come? Well, 2n is always even and if you add 1 to an even number you get an odd one. Next, the consecutive odd integer to 2n+1 is 2n+3 (2 away) Finally Pythagoras' theorem applied to this problem (2n+3)^2=(2n+1)^2+20 Solve for n Title: math challenge question conseutive odd integers right triangle probably pythagorean thorem? Post by: mikebrown on Sep 3, 2012 let x be the 2nd leg and x+2 be the hypotenuse
given that 20 is the first leg; x is the 2nd and third is the hypotenuse, we can come up with the phytagorean theorem c²=a²+b² (3 sides of a triangle) c=hypotenuse, a and b are the sides (x+2)²= 20² + x² x² + 4x + 4 = 400 + x² by transposition; x²-x² + 4x=400-4 4x= 396 x=396/4 x=99 ( this is the second leg) since hypotenuse is x+2 and the value of x=99; hypotenuse = 99 + 2 = 101 |