SOLUTION: 1. Find two consecutive whole numbers whose product is 156? 2.The sum of a number and its reciprocal is 25/12. Find the number and its reciprocal?

Question 890223: 1. Find two consecutive whole numbers whose product is 156? 2.The sum of a number and its reciprocal is 25/12. Find the number and its reciprocal? 3.The area of a triangle is 135cm2. if the altitude is 1/3 the base, what are lengths of the altitude and the base?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Find two consecutive whole numbers whose product is 156?
n(n+1) = 156
n^2 + n = 156
n^2 + n - 156 = 0
Factors to
(n+13)(n-12) = 0
positive solution
n = 12, and 13 are the two numbers
:
2. The sum of a number and it's reciprocal is 25/12
n + =
multiply by 12n, cancel the denominators and you have:
12n^2 + 12 = 25n
12n^2 - 25n + 12 = 0
Use the quadratic formula, leave the solutions in fractions
I got
n =
and
n =
Either one will work
:
3.The area of a triangle is 135cm2. if the altitude is 1/3 the base, what are lengths of the altitude and the base?
A = b*h
let a = the altitude, the b = 3a
*3a*a = 135
multiply both sides by 2
3a^2 = 270
Divide both sides by 3
a^2 = 270/3
a^2 = 90
a =
extract the square root of 9
a = is the altitude
and then b is 3 times that
b = is the base
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