Pythagorean Theorem: A rectangular park is 6 miles long and 5 miles wide. How long is a pedestrian route that runs diagonally ac
ross the park?
explain/show steps please
explain/show steps please
1 answer:
Answer: The exact length is sqrt(61) miles which approximates to 7.8102 miles
================================================
Work Shown:
See the attached image below. Draw a rectangle that is 6 by 5. Then add a diagonal line to represent the pedestrian route. This forms a right triangle. The right triangle has legs of 6 and 5. The hypotenuse is unknown, which we'll call x.
a = 6
b = 5
c = x
Use the pythagorean theorem to solve for x
a^2 + b^2 = c^2
6^2 + 5^2 = x^2
36 + 25 = x^2
61 = x^2
x^2 = 61
x = sqrt(61) which is the exact length
x = 7.8102 which is the approximate length
You might be interested in
Answer: A. Factor 2 => 4x greater
Factor 3 => 9x greater
Factor 5 => 25x greater
Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:
A = 2.π.r.h
A cylinder of radius r and height h has area:
= 2πrh
If multiply both dimensions <u>by a factor of 2</u>:
= 2.π.2r.2h
= 8πrh
Comparing to
:
=
= 4
Doubling radius and height creates a surface area of a cylinder 4 times greater.
<u>By factor 3:</u>
Comparing areas:
=
= 9
Multiplying by 3, gives an area 9 times bigger.
<u>By factor 5</u>:
Comparing:
=
= 25
The new area is 25 times greater.
B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.