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 no 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, that would be great.
To find the perimeter of the fence, you need to add up the lengths of all four sides.
Given that the width of the fence is (3√5)/√7 meters and the length is (2√3)/√5 meters, to calculate the perimeter, we can use the formula:
Perimeter = 2 * (width + length)
Plugging in the values, we get:
Perimeter = 2 * [(3√5)/√7 + (2√3)/√5]
To simplify this expression, we need to rationalize the denominators. To rationalize the denominator of each term, we multiply the numerator and denominator of each term by the conjugate of the denominator.
For the first term, multiply the numerator and denominator by √7:
[(3√5)(√7)/(√7)] = (3√35)/√7
For the second term, multiply the numerator and denominator by √5:
[(2√3)(√5)/(√5)] = (2√15)/√5
Now, substitute this back into the original expression for the perimeter:
Perimeter = 2 * [(3√35)/√7 + (2√15)/√5]
= 2 * [(3√35)/√7] + 2 * [(2√15)/√5]
= (6√35)/√7 + (4√15)/√5
To combine the two terms, we need to rationalize the denominators again, just like we did before. Multiplying the numerator and denominator of each term by the appropriate conjugate:
For the first term, multiply the numerator and denominator by √7:
[(6√35)(√7)/(√7)] = (6√245)/√7
For the second term, multiply the numerator and denominator by √5:
[(4√15)(√5)/(√5)] = (4√75)/√5.
Now, simplify the expression:
Perimeter = (6√245)/√7 + (4√75)/√5
= (6√245)/(√7/√7) + (4√75)/(√5/√5)
= (6√245)/1 + (4√75)/1
= 6√245 + 4√75
So, the exact perimeter of the fence is 6√245 + 4√75 meters.
Therefore, the correct answer is option D. 6√5 + 4√3 meters.