Asked by Anonymous
Draw a rectangle in which each diagnol=6cm and the acute angle between them is 45
Answers
Answered by
Reiny
In a rectangle, the two diagonals right-bisect each other.
Since they are equal, and we are told the angle between them is 45°, our rectangle must be a square.
let the side of the square be x
x^2 + x^2 = 6^2
2x^2 = 36
x^2 = 18
x = √18 = 3√2 or appr 4.26 cm
The other way would be to draw 2 lines that are perpendicular. If you have a compass, set the radius at 3 cm and draw a circle. Join the 4 intersection point and you will have your rectangle (square).
The diameter of the circle will be 6 cm, which in turn will be the diagonal of your square.
Since they are equal, and we are told the angle between them is 45°, our rectangle must be a square.
let the side of the square be x
x^2 + x^2 = 6^2
2x^2 = 36
x^2 = 18
x = √18 = 3√2 or appr 4.26 cm
The other way would be to draw 2 lines that are perpendicular. If you have a compass, set the radius at 3 cm and draw a circle. Join the 4 intersection point and you will have your rectangle (square).
The diameter of the circle will be 6 cm, which in turn will be the diagonal of your square.
Answered by
Steve
In a square (or rhombus), the diagonals are perpendicular.
Since your diagonals have a 45° angle between them, the two semi-diagonals form an isosceles triangle with vertex angle 45° and equal sides of length 3.
I expect you can draw that, eh? The length is 5.544 and the width is 2.296
Since your diagonals have a 45° angle between them, the two semi-diagonals form an isosceles triangle with vertex angle 45° and equal sides of length 3.
I expect you can draw that, eh? The length is 5.544 and the width is 2.296
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.