A landowner wishes to construct a fence around a small section of her property. The fence is rectangular and is (3√5)/√7 meters wide and (2√3)/√5 meters long. What is the exact perimeter of the fence? (Recall that the perimeter is the sum of each individual side of a shape.)
A.√5+√3 meters
B.(3√35)/7+(2√15)/5 meters
C.(6√35)/7+(4√15)/5 meters
D.6√5+4√3 meters
I did B. and got it wrong, so I know it is not that, but when I divide the radical, I don't get any of the answers. Please help!
Also, if you can provide a walk through, it would be great.
I know how to do up until I get to (3√35)/7, and (2√15)/5. But I do not know what to do after that.
It would be great if someone could answer as soon as possible.
My next answer is C., but can someone please check it to see if it is correct.
perimeter= 2L+2
= 2* 3√5)/√7 + 2*(2√3)/√5
= 6*sqrt35 /7 + 4 sqrt 15/5
That looks like C
Thank you,bobpursley. You are good at this, I have doing this problem for a while now, and it looks like it has been solved. Some of the posts before, are this same problem with more things added to is, so don't pay attention to the ones that say Dividing radicals before this one. Thank you again, you saved me a lot of time.
To find the perimeter of the fence, we need to add up the lengths of all four sides.
Given that the fence is rectangular, we know that opposite sides are equal in length.
The width of the fence is given as (3√5)/√7 meters.
The length of the fence is given as (2√3)/√5 meters.
To simplify these expressions, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
For the width, multiply both numerator and denominator by (√7):
(3√5)/√7 * (√7)/(√7) = (3√35)/√49 = (3√35)/7 meters
For the length, multiply both numerator and denominator by (√5):
(2√3)/√5 * (√5)/(√5) = (2√15)/√25 = (2√15)/5 meters
Now, we can determine the perimeter by adding up the four sides:
Perimeter = (3√35)/7 + (2√15)/5 + (3√35)/7 + (2√15)/5
Combining like terms, we get:
Perimeter = [(3√35 + 3√35) / 7] + [(2√15 + 2√15) / 5]
Perimeter = (6√35 / 7) + (4√15 / 5)
Hence, the exact perimeter of the fence is (6√35)/7 + (4√15)/5 meters.
Therefore, the correct answer is option C. (6√35)/7 + (4√15)/5 meters.