Question

The City Commission wants to construct a new street that connects Main Street and North Boulevard, as shown in the diagram below.

Not drawn to scale

a. What will be the length of the new street? Explain how you found this length.
b. The construction cost has been estimated at $140 per linear foot. Estimate the cost for constructing the street. Explain your method for finding the estimate.

Answer 1

This is the LAST question! please! someone help :/

Answer 2

a. It forms a right triangle, so you can use Pythagorean Theorem.
\(a^2 + b^2 = c^2\)

Answer 3

Thanks! do you know what the answer to "b." is?

Answer 4

b. You have a rate, the $/ft, and you find the length in part a) for the ft.
If you multiply them together, then you should get the cost, kind of like:
\(\Large \frac{$}{ft} * ft = $ \)

Answer 5

sooo can you please just give me the answer and show the work.. I'll understand it way better.

Answer 6

Did you get the \(c\)-value for (a)? And if so, what did you get?

Answer 7

No i didnt.. :'c

Answer 8

Hmm.. you should try to get that answer first. :P
All you have to do is plug in \(a=9\) and \(b=4\), since these are the legs of the right triangle, and then solve for \(c\) by taking the positive root. :)

Answer 9

\( a^2 + b^2 = c^2 \)

Answer 10

so its 9^2+4^2=13^2?

Answer 11

Im just trying to help my daughter out i forgot how to do all of this

Answer 12

please, i only have a few minutes..

Answer 13

well, we don't know the c-value.
9^2 + 4^2 = c^2
81 + 16 = c^2
97 = c^2 positive square root since negative lengths don't make sense
c = sqrt(97)

Then, I guess there's a few ways you could 'estimate' it, depending on how accurate you want to be.
I guess a pretty rough estimate would be considering that
\(\sqrt{81} < \sqrt{97} < \sqrt{100}\), so its pretty close to 10 (if you calculate it, its about 9.85, actually).
Then multiplying the rate, 140, by 10, we get ~$1400 as a pretty rough estimate.

Answer 14

Thanks :)

Answer 15

You're welcome. :)