Answer:
a = 3
b = 6
The product ab = 3 x 6 = 18
Step-by-step explanation:
Data Given:
Fraction of the area of Fido's yard =
Let X be the side of the hexagon.
So, the area of the Hexagon is:
Area of the Hexagon =
Now, we have to calculate the length of Fido's Leash by using Lw of Sine
Law of Sine = = =
=
Solving for Length, where sin30 = 1/2 and sin60 =
Suppose Length = Y
Y = X
Now, as we have got the length we can calculate the area that Fido can cover,
So, the area covered by Fido = x
Area = x
Area = x x
So, now, we can get the fraction of the area of Fido's Yard by dividing the area of hexagon by area that fido can cover.
Fraction of the area of Fido's yard =
x x /
x /
6 /
/
Which can be rewritten as by multiplying and dividing by
/ 6
By comparing the above equation and the given equation we can find a and b :
So,
a = 3
b = 6
And the product ab = 3 x 6 = 18