Finding diagonal of inscribed rectangle

In summary, We have an inscribed rectangle ABCD in a quadrant with distance CD marked as 3m. The length of AD can be found by drawing a diagonal from C to B and using the Pythagorean theorem to find the length of the diagonal, which is equal to the radius of the quadrant. This is because in a rectangle, the diagonals are equal. So, CB = AD and the length of AD can be calculated using the Pythagorean theorem.
  • #1
Ein Krieger
34
0

Homework Statement


A quadrant contains an inscribed rectangle ABCD. Given the distance marked: CD=3m , what is length of AD?




Homework Equations



Area of circle = pi*r^2
Pythagorean 's theorem : a^2=b^2+c^2

The Attempt at a Solution



We can draw diagonal from C to B similar to that from A to D. And that diagonal is equal to radius which is 10. Correct?
 
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  • #2
Correct. Do you know the reason it is correct? I mean, what is the reason that CB = AD?
 
  • #3
verty said:
Correct. Do you know the reason it is correct? I mean, what is the reason that CB = AD?

be cause it is a rule for all rectangles?
 
  • #4
Yes indeed. The diagonals of a rectangle are equal. A rhombus and parallelogram do not have equal diagonals, this is special to a rectangle.
 

1. What is an inscribed rectangle?

An inscribed rectangle is a rectangle that is drawn inside a larger shape, such as a circle or a triangle, so that all four of its vertices touch the edges of the larger shape.

2. Why is finding the diagonal of an inscribed rectangle important?

Finding the diagonal of an inscribed rectangle can be useful in many geometric calculations, such as finding the area or perimeter of the rectangle, or determining the distance between two points on the rectangle.

3. How can I find the diagonal of an inscribed rectangle?

The diagonal of an inscribed rectangle can be found using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two sides of the rectangle. So, the formula for finding the diagonal is √(a² + b²), where a and b are the lengths of the two sides of the rectangle.

4. Can I use any method other than the Pythagorean theorem to find the diagonal?

Yes, there are other methods that can be used to find the diagonal of an inscribed rectangle, such as using trigonometric functions or the distance formula. However, the Pythagorean theorem is the most commonly used and simplest method.

5. Are there any real-life applications of finding the diagonal of an inscribed rectangle?

Yes, there are many real-life applications of finding the diagonal of an inscribed rectangle, such as in construction, engineering, and architecture. It is also used in various fields of science, such as astronomy and biology, to calculate distances and measurements.

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