Answer:
Area of Mrs. Rockwell's lot is equal to the area of Mr. Brown's lot
Step-by-step explanation:
We can suppose the dimensions of Mrs. Rockwell's lot to be:
Length = x
Width = y
Then, we can write the dimensions of Mr. Brown's lot as:
Length = half as long as Mrs. Rockwell's lot
Length = 0.5x
Width = twice as wide as Mrs. Rockwell's lot
Width = 2y
Area of Mrs. Rockwell's lot = Length * Width
= x*y
Area of Mrs. Rockwell's lot = xy
Area of Mr. Brown's lot = 0.5x*2y
Area of Mr. Brown's lot = xy
<u>Area of Mrs. Rockwell's lot </u><u>is equal</u><u> to the area of Mr. Brown's lot, as calculated above</u>.
Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.
Now, Pythagoras' Theorem is defined as follows:
c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:
c^2 = a^2 + b^2
24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)
b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)
b = √(24^2 - 8^2) (Take the square root of both sides)
b = √512 (Evaluate 24^2 - 8^2)
b = 16√2 (Simplify √512)
= 22.627 (to three decimal places)
I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.
1) neither
2) geometric sequence
