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!

AnonymousConfusedGuy
Mar 16, 2018

#1**+2 **

Omi answered the second one in your earlier post

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

CPhill
Mar 16, 2018