SOLUTION: find the length of the diagonal a. a square in terms of its edge b. a rectangle in terms of its base b and its altitude h c. find the area of an equilateral triangle of side a

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Question 375801: find the length of the diagonal
a. a square in terms of its edge
b. a rectangle in terms of its base b and its altitude h
c. find the area of an equilateral triangle of side a
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem,
a)s%5E2%2Bs%5E2=d%5E2
highlight%28+d=sqrt%282%29%2As%29
.
.
b)b%5E2%2Bh%5E2=d%5E2
highlight%28+d=sqrt%28b%5E2%2Bh%5E2%29%29
.
.
.
c)Use Heron's formula,A=sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29
In this case, b=c=a
s=%281%2F2%29%28a%2Ba%2Ba%29=%283%2F2%29a
s-a=%281%2F2%29a
A=sqrt%28%283%2F2%29a%281%2F2%29a%281%2F2%29a%281%2F2%29a%29
A=sqrt%28%283%2F16%29%29a%5E4%29
highlight%28+A=%28sqrt%283%29%2F4%29a%5E2%29