Geometry

[sekaperkins22]

sorry i kept trying to draw the figure but it would not copy. So far i tried to use trigonometric ratio but i cant figure how to use the formula. In the diagram the two steel cables are each represented with the square root of 10900 along the slopes. and i dont know how they came up with answer c. What happened to the 5000, if i cut that value in half wouldn't they each weigh 2500? how did they come up with 250? Then in the square root, how come they divided the square root of 109 by 109? What confuses me is how to understand "the number of pounds per foot". How do i understand that? Thank you for your help-Brenda


The suspension bridge in the diagram above uses two steel
cables, each with a length of 10900 feet. The total weight
of the two cables is 5000 pounds. Which of the following
expressions represents the number of pounds per foot of
cable?

A. 2.5 square root of 109 divided by 109

B. 5 square root of 109 divided by 109

C. 250 square root of 109 divided by 109

D. 500 square root of 109 divided by 109

 

[soroban]

Hello, sekaperkins22!

You gave two descriptions of the cable lengths.

In the diagram the two steel cables are each represented with the square root of 10900 along the slopes.

The suspension bridge in the diagram above uses two steel cables, each with a length of 10900 feet.
The total weight of the two cables is 5000 pounds.
Which of the following expressions represents the number of pounds per foot of cable?

. . \(\displaystyle (A)\;\frac{2.5\sqrt{109}}{109} \qquad(B)\;\frac{5\sqrt{109}}{109} \qquad (C)\; \frac{250\sqrt{109}}{109} \qquad (D)\;\frac{500\sqrt{109}}{109}\)

Besides the glitch in typing, I don't see any difficulty.
You've never "rationalized a denominator" before? .Ever?


\(\displaystyle \text{Assuming the lengths are }\sqrt{10,900} \:=\:10\sqrt{109}\text{ feet,}\)
. . \(\displaystyle \text{we have: }\:2 \times 10\sqrt{109} \:=\: 20\sqrt{109}\text{ feet of cable.}\)

\(\displaystyle \text{Then: }\:\frac{5000\text{ lbs}}{20\sqrt{109}\text{ ft}} \;=\;\frac{250}{\sqrt{109}}\text{ lbs/ft}\)


\(\displaystyle \text{Multiply by }\frac{\sqrt{109}}{\sqrt{109}}\!:\;\;\frac{250}{\sqrt{109}}\cdot \frac{\sqrt{109}}{\sqrt{109}} \;=\;\frac{250\sqrt{109}}{109}\)


\(\displaystyle \text{Got it?}\)