Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4"

(Solution)
(Solution)
 
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let <math>\sqrt{y^{2} - x^{2}}</math> be z.
 
let <math>\sqrt{y^{2} - x^{2}}</math> be z.
  
So x*z=<math>39\sqrt95</math>
+
So x* <math>\sqrt{y^{2} - x^{2}}</math> = <math>39\sqrt{95}</math>
  
 
Here x = 13 satisfies with y = 32  { By Hit And Trial Method }
 
Here x = 13 satisfies with y = 32  { By Hit And Trial Method }

Latest revision as of 06:39, 9 August 2019

Problem

Suppose ABCD is a parallelogram with area $39\sqrt{95}$ square units and $\angle{DAC}$ 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 $\sqrt{y^{2} - x^{2}}$

let $\sqrt{y^{2} - x^{2}}$ be z.

So x* $\sqrt{y^{2} - x^{2}}$ = $39\sqrt{95}$

Here x = 13 satisfies with y = 32 { By Hit And Trial Method }

so Perimeter is 2(13+32) $\Rightarrow{\boxed {90}}$

See also

2018 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions