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# Two last questions

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1:  A square and an equilateral triangle have equal perimeters. The area of the triangle is 2 sqrt 3 square inches. What is the number of inches in the length of the diagonal of the square?

2:  In triangle ABC, AB = AC = 5 and BC = 6. Let O be the circumcenter of triangle ABC. Find the area of triangle OBC. (The answer involves one or more fractions)

Also I take it back there might be on more problem after this.

Thanks to everyone who has or will help!

Mar 16, 2018

#1
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For the first  one

1:  A square and an equilateral triangle have equal perimeters. The area of the triangle is 2 sqrt 3 square inches. What is the number of inches in the length of the diagonal of the square?

Area  of triangle  is given by

2sqrt (3)  =  (1/2) side^2  * sin (60)

2 sqrt (3)  =  (1/2)side^2  * sqrt (3) / 2       simplify

2  = side^2 / 4

8  = side^2

√8  = side

So....the perimeter of the triangle   = 3√8  in

So.......the  side of the square  =  1/4  of this   =  (3/4)√8  in

And the diagonal  is √2  of this  =  √2 *  (3/4) √8  =   (3/4) * √16  in  =

(3/4)* 4   =    3 in   Mar 16, 2018
edited by CPhill  Mar 16, 2018
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Thanks!

AnonymousConfusedGuy  Mar 16, 2018
edited by AnonymousConfusedGuy  Mar 16, 2018