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Question 1:

We have a 45-45-90 right triangle with the hypotenuse being the length from one corner to the opposite corner.

Multiply 30 ft with the square root of 2 and use a calculator to help give you numerical value to get your answer.

[tex]30 \sqrt{2} \approx 42[/tex]

Your answer is the second choice.

Question 2:

The equilateral triangle can be divided into 2 30-60-90 triangles with the longer leg being the altitude. To get half of the side length of the right triangle, divide the altitude by the square root of 3.

[tex]\dfrac{15}{ \sqrt{3} }=\dfrac{15 \sqrt{3} }{3}=5 \sqrt{3} [/tex]

The full side length is double of that, which is [tex]10 \sqrt {3}[/tex].

Multiply that by 3 to get the full perimeter.
[tex]10 \sqrt{3}*3=30 \sqrt{3}[/tex]

Your answer is the third choice. Hope this helps! :)
choixongdong
lets c = # of feet person walks from one corner to the opposite corner
as you know it's a square so when you draw a line from one corner to the opposite corner, it'll divide into 2 equal right triangles with side = 30ft
so
c^2 = 30^2 +30^2
c^2 = 900 + 900
c^2 = 1800
c = √1800
c = 42 ft (round to nearest foot)

answer is B. 42 ft
---------------------------
h = altitude = 15 m,
and a = side of equilateral triangle

equilateral triangle so all angles are equal and equal to 60 degrees and all sides are also equal

so
sin(60) =  15/a
a = 15 / sin(60)
a =10√3

P = 3a
P = 3(10√3)
P = 30√3

answer
C)  30√3 m

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