# 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:

**Showing 1 comment:**

**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.

Tips for related online calculators

Are you looking for help with calculating roots of a quadratic equation?

Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.

Check out our ratio calculator.

Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?

Calculation of an equilateral triangle.

See also our trigonometric triangle calculator.

Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.

Check out our ratio calculator.

Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?

Calculation of an equilateral triangle.

See also our trigonometric triangle calculator.

#### 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

## Related math problems and questions:

- Ratio of sides

Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in a ratio of 2 to 7. - Interesting property

Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle? - Triangles

An equilateral triangle with a side 16 cm has the same perimeter as an isosceles triangle with an arm of 23 cm. Calculate the base x of an isosceles triangle. - Midpoints

Triangle whose sides are midpoints of sides of triangle ABC has a perimeter 64. How long is the perimeter of the triangle ABC? - Rectangle - sides ratio

Calculate the area of a rectangle whose sides are in ratio 9:14 and perimeter is 388. - The circumference

The circumference of the rectangle is 62 cm. A square whose side is as long as one side of a rectangle has a circumference of 56 cm. What is the area of each shape? - Irregular hexagon

There is an irregular hexagon whose sides are the same length. The opposite sides are parallel; their distance is 237, 195, and193. What is its area? - Perimeter+mixed

Find the perimeter of a triangle whose sides are 5 1/2 cm, 7 3/5 cm, and 3 1/4 cm, respectively. - Rectangles

The perimeter of a rectangle is 90 m. Divide it into three rectangles. The shorter side has all three rectangles the same. Their longer sides are three consecutive natural numbers. What are the dimensions of each rectangle? - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with the same circumference so that these circumferences are as small as possible. - Perimeter 7778

The triangle has 7 cm, 8 cm, and 5 cm long sides. How long is the side of a square with the same perimeter as a triangle? - Circumference 6338

The circle has the same area as the square, whose circumference is 400m. Calculate the diameter of the circle. - Perimeters

A rectangle has a perimeter of 16p centimeters. It had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8. - Find all

Find all right-angled triangles whose side lengths form an arithmetic sequence. - Circumference 7655

The triangle has a circumference of 35 cm. One side is four times longer than the other and, at the same time, 1 cm longer than the third. Determine the sides of the triangle. - Triangle perimeter

Calculate the triangle perimeter whose sides are in ratio 3:5:7 and the longest side is 17.5 cm long. - Equilateral cone

We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?