Part 1: Find the area of a rectangular object which has a length of 5√8 inches and a width of 2√5 inches. (3 points)
Part 2: Explain, in complete sentences, how you arrived at the simplified answer and give the final solution in simplified radical form. (2 points)
Part 3: What type of object in your home or school might this be? (1 point)
1. area is length * width
5√8 * 2√5 = 10√40 = 20√10
I'll let you handle parts 2 and 3.
Part 1: To find the area of a rectangular object, we multiply the length by the width. In this case, the length is 5√8 inches and the width is 2√5 inches. Therefore, the area is:
Area = Length x Width
Area = (5√8 inches) x (2√5 inches)
= 10√8√5 square inches
= 10√(8 x 5) square inches
= 10√40 square inches
Part 2: To simplify the answer, we need to find the largest perfect square factor of 40. Since 4 is a perfect square and divides 40, we can simplify the radical:
10√40 square inches = 10√(4 x 10) square inches
= 10(2√10) square inches
= 20√10 square inches
So, the final solution in simplified radical form is 20√10 square inches.
Part 3: An object with the given dimensions could be a rectangular picture frame, a book cover, or a wall-mounted shelf, among other possibilities.