The area of a larger square is 16 times the area of the smaller square. How many times as long is the base of the larger square than the base of the smaller square?
side of small square --- x
area of small square --- x^2
area of larger square = 16x^2
side of larger square = √(16x^2) = 4x
side of larger is 4 times the side of the smaller
notice that the areas of similar squares are proportional to the square of the their sides
Let's assume that the base of the smaller square is "x" units.
The area of the smaller square will be x^2 square units.
According to the given information, the area of the larger square is 16 times the area of the smaller square, which means:
Area of larger square = 16 * Area of smaller square
Area of larger square = 16 * x^2 square units
Since the larger square is a square, all sides are equal in length. Let's assume the base of the larger square is "y" units.
Therefore, the area of the larger square can be written as y^2 square units.
Using the information from above:
y^2 = 16 * x^2
To find how many times longer the base of the larger square is compared to the base of the smaller square, we need to find the ratio of y to x.
Dividing both sides of the equation by x^2:
(y^2)/(x^2) = (16 * x^2)/(x^2)
Simplifying:
(y/x)^2 = 16
Taking the square root:
y/x = √16
y/x = 4
Therefore, the base of the larger square is 4 times longer than the base of the smaller square.
To find out how many times longer the base of the larger square is compared to the smaller square, we need to compare their lengths.
Let's assume the base of the smaller square is 'x'. Therefore, the area of the smaller square is x^2 since the area of a square is given by the formula A = side^2.
According to the given information, the area of the larger square is 16 times the area of the smaller square. So, the area of the larger square can be expressed as 16x^2.
To find the base of the larger square, we need to take the square root of the area, since the area of a square is equal to the side length squared. Therefore, the base of the larger square would be √(16x^2) = 4x.
Now we can compare the bases of the two squares. The base of the larger square is 4x, and the base of the smaller square is x.
To determine how many times longer the base of the larger square is compared to the smaller square, we can divide the base of the larger square by the base of the smaller square: (4x) / x = 4.
Hence, the base of the larger square is 4 times longer than the base of the smaller square.