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
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