Suppose a circle has a radius of 13 inches. How far would a 24 inch chord be from the center of the circle? (Hint: Draw a diagra
2 answers:
Answer:
Step-by-step explanation:
Directions
- Draw a circle
- Dear a chord with a length of 24 inside the circle. You just have to label it as 24
- Draw a radius that is perpendicular and a bisector through the chord
- Draw a radius that is from the center of the circle to one end of the chord.
- Label where the perpendicular radius to the chord intersect. Call it E.
- You should get something that looks like the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.
Givens
AC = 13 inches Given
CB = 24 inches Given
CE = 12 inches Construction and property of a midpoint.
So what we have now is a right triangle (ACE) with the right angle at E.
What we seek is AE
Formula
AC^2 = CE^2 + AE^2
13^2 = 12^2 + AE^2
169 = 144 + AE^2 Subtract 144 from both sides.
169 - 144 = 144-144 + AE^2 Combine
25 = AE^2 Take the square root of both sides
√25 = √AE^2
5 = AE
Answer
The 24 inch chord is 5 inches from the center of the circle.
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Answer:
Length:8 m
Width:3 m
Step-by-step explanation:
<u><em>The complete question is</em></u>
If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.
step 1
<em>Perimeter of rectangle</em>
we know that
The perimeter of rectangle is equal to
we have
so
Simplify
-----> equation A
step 2
Perimeter of triangle
The perimeter of triangle is equal to
so
Multiply by 2 both sides
----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (8,3)
see the attached figure
therefore
The dimensions of the rectangle are
Length:8 m
Width:3 m
Answer:
the ratio is 9: 25
Step by step calculation: