# 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 b

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 b

^{2}-1,5b+SR=0and 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:

We encourage you to watch this tutorial video on this math problem: video1

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