Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4"
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| − | == Solution (Involves Hit and Trial) | + | == Solution == |
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| + | (Involves Hit and Trial) | ||
Let any one side be x and other side be y. | Let any one side be x and other side be y. | ||
| − | Then one diagonal is | + | Then one diagonal is <math>{</math>{y}<math> </math>^<math> </math>2<math> </math>-<math> </math>{x}<math> </math>^<math> </math>2<math>}</math> <math>^</math> <math>{1 </math>/<math> 2}</math> |
let [(y)^2-(x)^2]^(1/2) be z. | let [(y)^2-(x)^2]^(1/2) be z. | ||
Revision as of 06:25, 9 August 2019
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 ${$ (Error compiling LaTeX. Unknown error_msg){y}$$ (Error compiling LaTeX. Unknown error_msg)^$$ (Error compiling LaTeX. Unknown error_msg)2$$ (Error compiling LaTeX. Unknown error_msg)-$$ (Error compiling LaTeX. Unknown error_msg){x}$$ (Error compiling LaTeX. Unknown error_msg)^$$ (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 | ||
