Question

Which one and what do I put in the box(s)

Answer 1

Answer:

Option A i the right option.

First blank is 110-$10\sqrt{61}$ or 10(11-$\sqrt{61}$)

Second blank is 31.898

Let me know if anything didn't make sense.  

Step-by-step explanation:

So a diagonal through a rectangle makes two triangles.  The question wants to know how much walking is saved walking down the diagonal  vs walking along two sides that make the diagonal.  in this case the two non diagonal sides walked are 60 paces and 50 paces.

A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.  

c^2 = 60^2 + 50^2

c = $\sqrt{60^2 + 50^2}$

c = $\sqrt{6100} = 10\sqrt{61}$

if you don't get how to simplify a radical like that let me know.

Anyway, looking at the answers you can see right away the second option says no approximation is necessary.  Well, you need to approximate square root of 61, so we can say the second answer is not right.  So now we need to know what to fill in for option 1.

it wants the distance saved, well we know the distance of the diagonal is $10\sqrt{61}$  Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.

Now, to find the difference, that is subtraction.  So subtract the smaller number from the larger number.  You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse.  so that's 110-$10\sqrt{61}$.  That is the exact form.  Or you could use 10(11-$\sqrt{61}$)  They are the same.

Then just plug that into a calculator for a decimal approximation.