2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4
Problem
Suppose ABCD is a parallelogram with area square units and
is a right angle. If the lengths of all the sides of ABCD are integers, what is the perimeter of ABCD?
Solution
(Involves Hit and Trial) Let any one side be x and other side be y.
Then one diagonal is ${{y}$ (Error compiling LaTeX. Unknown error_msg)^-
^$2}$ (Error compiling LaTeX. Unknown error_msg) $^$ (Error compiling LaTeX. Unknown error_msg) ${1$ (Error compiling LaTeX. Unknown error_msg)/$2}$ (Error compiling LaTeX. Unknown error_msg)
let [(y)^2-(x)^2]^(1/2) be z.
So x*z=39*95^(1/2)
Here x = 13 satisfies with y = 32 { By Hit And Trial Method }
so Perimeter is 2(13+32)=90
See also
2018 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |