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

(Solution)
(Solution)
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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 <math>\sqrt{</math>y^{2}<math> </math>-<math> </math>x^{2}<math>}</math>
+
Then one diagonal is \sqrt{<math>y^{2}</math> <math>-</math> <math>x^{2}</math>}
  
 
let [(y)^2-(x)^2]^(1/2) be z.
 
let [(y)^2-(x)^2]^(1/2) be z.

Revision as of 06:33, 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 [(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 (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