Q:The ratio of the perimeters of two square is 5 to 4. If the area of the smaller square is 36 units, what is the area of the larger square?

A: 56.25

My teacher told us the answer, 56.25, so that we could correct it. But I don't understand how she got the answer at all, so can someone please help me solve the question so that I could understand how to do it.

can someone please help me :0

a1 = the side length side of the smaller square

a2 = the side length side of the larger square

The area of the smaller square is 36

A1 = a1 ^ 2 = 36

a1 ^ 2 = 36

a1 = sqrt ( 36 ) = 6

Perimeter of square = 4 side length

In this case :

4 a2 / 4 a1 = 5 / 4

a2 / a1 = 5 / 4

a2 / 6 = 5 / 4 Multiply both sideas by 6

a2 = 5 * 6 / 4 = 30 / 4 = 15 / 2 = 7.5

The area of the larger square :

A2 = a2 ^ 2 = 7.5 ^ 2 = 56.25

thank you :D

a1 = the length side of the smaller square

a2 = the length side of the larger square

To solve this problem, we can use the given information about the ratio of the perimeters and the area of the smaller square.

Let's start by finding the side length of the smaller square. We know that the area of the smaller square is 36 units, so we can use the formula for the area of a square:

Area of smaller square = side length * side length = 36

Let's solve this equation for the side length:

(side length)^2 = 36

Taking the square root of both sides, we get:

side length = √36
= 6

Now that we have the side length of the smaller square, we can find the side length of the larger square using the ratio of the perimeters. The ratio of the perimeters is given as 5 to 4.

Let's denote the side length of the larger square as "x". We can set up the following equation using the ratio of the perimeters:

(Perimeter of smaller square) / (Perimeter of larger square) = 5/4

The perimeter of a square is given by 4 multiplied by the side length:

(4 * 6) / (4 * x) = 5/4

Simplifying this equation, we get:

24 / (4x) = 5/4

Cross-multiplying, we have:

4x * 5 = 24 * 4

20x = 96 (multiply and simplify)

x = 96/20

x = 4.8

Now that we have the side length of the larger square, we can find its area using the formula for the area of a square:

Area of larger square = side length * side length

Area of larger square = 4.8 * 4.8

Area of larger square ≈ 22.44

Therefore, the area of the larger square is approximately 22.44 units.