the areas of two squares are in the ratio 9:16. The smaller square has sides of length 15cm find the length of the sides of the larger square
areas proportional to square of length
so
lengths proportional to square root of areas
sqrt (9/16) = 3/4
so every length on the big one is 4/3 times the length on the little one.
To find the length of the sides of the larger square, we can use the given ratio of the areas.
Let's assume the length of the sides of the larger square is "x" cm.
The ratio of the areas is given as 9:16, which means the ratio of the side lengths squared is also 9:16:
(area of smaller square) / (area of larger square) = (side length of smaller square)^2 / (side length of larger square)^2
Using the given values, we can substitute the values:
(9/16) = (15)^2 / x^2
To solve for x, we can cross-multiply:
9 * x^2 = 16 * 15^2
9 * x^2 = 16 * 225
Divide both sides by 9:
x^2 = (16 * 225) / 9
x^2 = 16 * 25
x^2 = 400
Taking the square root of both sides:
x = √400
Therefore, the length of the sides of the larger square is 20 cm.
To find the length of the sides of the larger square, we need to use the information given about the ratio of their areas.
Let's denote the length of the sides of the larger square as "x" cm.
The area of a square is given by the formula: Area = side length squared.
So, we can find the area of the smaller square by calculating:
Area of smaller square = (15 cm)^2 = 225 square cm.
According to the ratio given, the areas of the two squares are in the ratio 9:16. Therefore, we can set up the following equation:
225 square cm (area of smaller square) / x^2 (area of larger square) = 9/16.
To solve this equation, we need to cross-multiply:
225 * 16 = 9 * x^2
3600 = 9 * x^2
Dividing both sides of the equation by 9:
400 = x^2
Taking the square root of both sides, we get:
20 = x
Hence, the length of the sides of the larger square is 20 cm.