2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4

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) $\Rightarrow{\boxed {90}}$

2018 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4

Problem

Solution

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