fence has dimensions of 8ft by 4ft. Each sections has a diagonal brace. What is the exact length of the brace?

Question

Want to know how to find the exact length of a diagonal brace of a fence. The dimensions of the fence is 8ft by 4ft.

Answer 1

 Since we are assuming that the section of fence is a rectangle, the diagonal would be the hypotenuse of a right triangle. The legs would be 4 feet and 8 feet. 

 

 Can you take it from here? If not, scroll down. 

 

 

 

Now we will use  The Pythagorean theorem.

a^2 + b^2 = c^2

 

 Need more help? Scroll down. 

 

4^2 + 8^2 = c^2

16 + 64 = c^2

80 = c^2

  Now take the square root of both sides. 

c = √80

 Do not stop there. 

 If you use your calculator now, you will get a rounded off answer. If your class requires the exact answer, you should keep your answer in square root form. However this square root can be simplified as follows:

 

√80 = √16 • √5

which = 4√5

 

 This is your exact answer in simplest form. 

Answer 2

Hey Randy,

 

It's not 80 ft. It's square root of 80 ft as a couple of others answered.

 

You can break down 80 ft to 16 X 5, the square root of which would be 4 X square root of 5. In your calculator, you'd do a square root of 80.

 

Thanks,

 

-Umar.

Answer 3

Hi Randy,

 

To find the length of the diagonal use the Pythagorean theorem equation.  This equation is a² + b^{2  =}  c². substitue  dimensions of the fence into the equation for a and b, then square each dimension, and then add those products together.  So 4 squared is 16 and 8 squared is 64.  When I add those I get a total of 80.

 

Now  equation is 80 = c² where c is the length of the diagonal.  To solve for c, take the square root of both sides of the equation and the result is 8.94 = c

Answer 4

When you want to find the diagonal of a rectangle, it is like finding the hypotenuse of a triangle when you know your side and base. So you must use the Pythagorean theorem (c²=a²+b²)