The perimeter of a square is 12cm greater than that of another square. It's area exceeds the area of the other by 39cm^2. Find the perimeter of each square. I don't get how to set this up.
let x be the side of the smaller square, area is x^2
then x+3 must be the side of the larger square.
(x+3)^2 -x^2=39
solve for x, and x+3
To solve this problem, let's set up some variables.
Let's say the side length of the first square is "x" cm. Therefore, the perimeter of the first square is 4x cm.
Let's also say the side length of the second square is "y" cm. Therefore, the perimeter of the second square is 4y cm.
According to the problem, the perimeter of the first square is 12 cm greater than that of the second square.
So, we can write the equation:
4x = 4y + 12 ----(Equation 1)
Additionally, the area of the first square exceeds the area of the second square by 39 cm^2.
The area of a square is calculated by squaring the length of one side. Therefore, the area of the first square is x^2 cm^2, and the area of the second square is y^2 cm^2.
So, we can write the equation:
x^2 = y^2 + 39 ----(Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y, which will give us the perimeter of each square.
To solve this problem, we need to set up a system of equations using the given information. Let's start by assigning variables to represent the unknown quantities.
Let's denote:
- The side length of the first square as 'x'.
- The side length of the second square as 'y'.
We know that the perimeter of the first square is 12 cm greater than the perimeter of the second square. The perimeter of a square is given by 4 times the length of its side. Therefore, we can write the equation:
4x = 4y + 12 (Equation 1)
We also know that the area of the first square exceeds the area of the second square by 39 cm^2. The area of a square is given by the length of its side squared. So we can write the equation:
x^2 = y^2 + 39 (Equation 2)
Now we have a system of equations with two unknowns. We can solve this system to find the values of x and y, which will give us the side lengths of the squares.
To solve the system of equations, we can use different methods such as substitution or elimination. Let's use the substitution method here.
From Equation 1, we can rearrange it as:
x = y + 3
Substituting this value of x into Equation 2, we get:
(y + 3)^2 = y^2 + 39
Expanding the equation, we have:
y^2 + 6y + 9 = y^2 + 39
Simplifying the equation by canceling out y^2 terms, we get:
6y + 9 = 39
Subtracting 9 from both sides, we have:
6y = 30
Dividing both sides by 6, we get:
y = 5
Now we can substitute this value of y back into Equation 1 to find x:
4x = 4(5) + 12
4x = 20 + 12
4x = 32
Dividing both sides by 4, we have:
x = 8
Therefore, the side length of the first square is 8 cm, and the side length of the second square is 5 cm.
To find the perimeters of the squares, we can use the formula: Perimeter = 4 * side length.
For the first square, the perimeter is:
Perimeter of first square = 4 * 8 = 32 cm
For the second square, the perimeter is:
Perimeter of second square = 4 * 5 = 20 cm
So, the perimeter of the first square is 32 cm, and the perimeter of the second square is 20 cm.