A piece of wire 168cm. long is to be cut into two pieces, each to be bent to make a square. The lenght of a side of one square is to be 2cm. greater than the lenght of aside of the other. What is the area of the smaller square? Ans= 80
Ah, I see we have a wire conundrum here! Let me put on my clown wig and help you out with a touch of humor.
First, let's break this down: we have a wire of length 168 cm, which we'll divide into two pieces to create two squares. One square has a side length that's 2 cm greater than the other.
Let's call the side length of the smaller square "x". Then the side length of the larger square will be "x + 2" because it's 2 cm longer, right?
Now, let's find the total length of the wire we'll need for the two squares. The wire length is 168 cm. Since we'll be using this wire for the perimeter of both squares, we can set up the following equation:
Perimeter of the smaller square + Perimeter of the larger square = Total wire length
4x + 4(x + 2) = 168
Simplifying this equation, we get:
4x + 4x + 8 = 168
8x + 8 = 168
8x = 160
x = 20
So, the side length of the smaller square is 20 cm.
Finally, we can find the area of the smaller square by squaring its side length:
Area of the smaller square = x^2 = 20^2 = 400
Therefore, the area of the smaller square is 400 square units. Voila!
Let's denote the length of the side of the smaller square as x cm.
According to the problem, the length of the side of the larger square is 2 cm greater than the length of the side of the smaller square. Therefore, the length of the side of the larger square is (x + 2) cm.
To find the area of a square, we square the length of its side. So, the area of the smaller square is x^2 square cm, and the area of the larger square is (x + 2)^2 square cm.
The wire length is the sum of the perimeters of both squares, which is equal to the sum of the lengths of all sides. The perimeter of a square is four times the length of its side.
So, we have the equation:
4x + 4(x + 2) = 168
Simplifying the equation:
4x + 4x + 8 = 168
8x + 8 = 168
8x = 160
x = 160/8
x = 20
Hence, the length of the side of the smaller square is 20 cm.
To find the area of the smaller square, we square the length of its side:
Area = x^2 = 20^2 = 400 square cm.
Therefore, the area of the smaller square is 400 square cm.
To find the area of the smaller square, we need to first determine the lengths of the sides of the two squares.
Let's assume the length of the side of the smaller square is x cm. Since the length of the side of the other square is 2 cm greater, the length of the side of the larger square will be (x + 2) cm.
Now, let's calculate the total length of the wire when it is cut into two pieces. Each square requires four sides, so the total length of the wire will be:
Total Length = 4x + 4(x + 2)
We know that the total length of the wire is 168 cm. Therefore, we can set up the following equation:
168 = 4x + 4(x + 2)
Let's simplify and solve for x:
168 = 4x + 4x + 8
168 = 8x + 8
160 = 8x
x = 20
Now that we have the value of x, we can find the length of the side of the larger square:
(x + 2) = 20 + 2 = 22 cm
Finally, we can calculate the areas of the squares:
Area of smaller square = x^2 = 20^2 = 400 sq. cm
Area of larger square = (x + 2)^2 = 22^2 = 484 sq. cm
Therefore, the area of the smaller square is 400 square cm.