Question 345954: one leg of a right triangle has a length of 3m. the other sides have lengths that are consecutive integers. find the lengths.
other leg=
hypotenuse=
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (n+1)^(2)=n^(2)+3^(2)
Since n^(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting n^(2) from both sides.
(n+1)^(2)-n^(2)=3^(2)
Squaring an expression is the same as multiplying the expression by itself 2 times.
(n+1)(n+1)-n^(2)=3^(2)
Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(n*n+n*1+1*n+1*1)-n^(2)=3^(2)
Simplify the FOIL expression by multiplying and combining all like terms.
(n^(2)+2n+1)-n^(2)=3^(2)
Since n^(2) and -n^(2) are like terms, add -n^(2) to n^(2) to get 0.
0+2n+1=3^(2)
Combine all similar terms in the polynomial n^(2)+2n+1-n^(2).
2n+1=3^(2)
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
2n=-1+3^(2)
Simplify the right-hand side of the equation.
2n=8
Divide each term in the equation by 2.
(2n)/(2)=(8)/(2)
Simplify the left-hand side of the equation by canceling the common factors.
n=(8)/(2)
Simplify the right-hand side of the equation by simplifying each term.
n=4
So, the hypotenuse is 5 meters,and the other leg is 4 meters.
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