An equivalent
An equilateral triangle has the same perimeter as a rectangle whose sides are b and h (b > h). Considering that the area of the triangle is three times the area of the rectangle. What is the value of b/h?
Correct answer:
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Math student
If I good understand the task:
Let a=1 (Side of Triangel)
oT=3 (perimeter of triangel)
ST=0,4330127... (Surface of Triangel)
SR=0,1433756...(Surface of Rectangel)
h=SR/b (h=shorter side of Rectangel, b=longer side of Rectangel)
Then b2-1,5b+SR=0
and b=1,39665480...; h=0,10335451929... and b/h=r=13,51446313...
True-false test:
b*h=0,1033451929...*1,39665480...=0,14433756=ST/3
2*(b+h)=2*(1,39665480+0,1033451929)=3.
Let a=1 (Side of Triangel)
oT=3 (perimeter of triangel)
ST=0,4330127... (Surface of Triangel)
SR=0,1433756...(Surface of Rectangel)
h=SR/b (h=shorter side of Rectangel, b=longer side of Rectangel)
Then b2-1,5b+SR=0
and b=1,39665480...; h=0,10335451929... and b/h=r=13,51446313...
True-false test:
b*h=0,1033451929...*1,39665480...=0,14433756=ST/3
2*(b+h)=2*(1,39665480+0,1033451929)=3.
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You need to know the following knowledge to solve this word math problem:
- algebra
- quadratic equation
- equation
- arithmetic
- square root
- planimetrics
- area of a shape
- perimeter
- triangle
- rectangle
- basic functions
- ratio
- numbers
- fractions
Units of physical quantities:
Grade of the word problem:
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