SOLUTION: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of
length 2S and width S as shown. What fraction of the area of the rectangle
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length 2S and width S as shown. What fraction of the area of the rectangle
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Question 1061957: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of
length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?
Image is in the link: http://prntscr.com/dkzrut Found 2 solutions by josgarithmetic, MathTherapy:Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website! How high is the equilateral triangle?
Base is S and the length of the other two of its sides also S each. Pythagorean Theorem formula will help; imagine cutting the triangle into two parts along the altitude.
, using "a" for the altitude length.
Area of the whole rectangle:
Fraction of the area which is uncovered:
-
Substitute for a:
The simplification algebra steps are not shown here, but final result should be .
You can put this solution on YOUR website! A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of
length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?
Image is in the link: http://prntscr.com/dkzrut
Area of rectangle:
Area of square:
Area of triangle:
Area uncovered:
Fraction of area uncovered:
(