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

Revision as of 06:36, 9 August 2019 by Jatsing (talk | contribs) (Solution)

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