Glen created a mural on a rectangular sheet of paper with a width of √18 feet and a length of √24.
A. Find the exact area of the mural, in simplified form.
When Glen’s mural was unveiled, the school made a smaller version of the mural to advertise the event. The replica’s length and width were half of the size of the original mural.
B. Find the exact area of the replica, in simplified form. Explain why you did each step.
A. To find the exact area of the mural, we need to multiply its length and width. Given that the width is √18 feet and the length is √24 feet, we can find the area using the formula:
Area = Length x Width
Area = (√24)(√18)
To simplify this expression, we can rewrite √24 and √18 in terms of their prime factors:
√24 = √(2^2 * 3) = 2√3
√18 = √(2 * 3^2) = 3√2
Now, substituting these values back into the formula, we get:
Area = (2√3)(3√2)
To find the product, we multiply the coefficients (2 and 3) and multiply the square roots (√3 and √2):
Area = 2 * 3 * (√3 * √2)
Area = 6√(3 * 2)
Area = 6√6
Therefore, the exact area of the mural, in simplified form, is 6√6 square feet.
B. If the replica's length and width are half the size of the original mural, we can find the area of the replica by halving the dimensions of the original mural and applying the same formula:
Original width = √18 feet
Original length = √24 feet
Replica width = (1/2) * √18
Replica length = (1/2) * √24
To find the area of the replica, we multiply the replica's length and width:
Replica area = (1/2) * √18 * (1/2) * √24
Simplifying this expression, we get:
Replica area = (1/4) * √2 * √3 * √2 * √2
Since √2 * √2 = 2, we further simplify to:
Replica area = (1/4) * 2 * √2 * √3
Finally, multiplying the coefficient and squareroots, we obtain:
Replica area = (1/2) * √6
Therefore, the exact area of the replica, in simplified form, is (1/2)√6 square feet.
A: LW = √18√24 = √(18*24) = √(2*3^2 * 2^3*3) = √(2^4 3^3) = 12√3
since A = LW, what if you have (L/2)(W/2)?