A wire of length 380 cm is cut into 10 pieces.Each piece is then bent to form a square.The dimensions of the first three smallest squares are shown below.Find the value of x and hence,the area of the eighth largest square.
x cm[ ] (x+1)cm [ ]
x cm (x+1)cm
(x+2)cm[ ]
(x+2)cm
Answer: x=5
Area=144cm
clearly the lengths of the sides are sequential integers, starting with x.
The sum of the perimeters is thus
4(10x + 9*10/2) = 40x+180 = 380
...
To find the value of x, we need to determine the side length of each square. We know that the length of the wire is 380 cm and it is divided into 10 pieces.
1. We can start by finding the length of each individual piece. We divide the total length of the wire (380 cm) by the number of pieces (10):
Length of each piece = 380 cm / 10 = 38 cm
2. Since each piece is bent to form a square, we need to find the side length of each square. The side length is the same as the length of each piece.
Side length of each square = 38 cm
3. Considering the given dimensions of the first three smallest squares, let's review:
- First square: x cm by x cm
- Second square: (x + 1) cm by (x + 1) cm
- Third square: (x + 2) cm by (x + 2) cm
4. We can now create an equation using these dimensions to find the value of x.
For the first square: x cm by x cm, the side length is x cm. We know that the side length is 38 cm, so we can set up the equation:
x = 38 cm
Solving this equation, we find that x = 38 cm.
5. Now that we have found the value of x, we can calculate the area of the eighth largest square.
The side length of the eighth largest square is (x + 7) cm. Substituting the value of x as 38 cm, we have:
Side length of the eighth largest square = (38 + 7) cm = 45 cm
Since the square has equal sides, the area is calculated by squaring the side length:
Area of the eighth largest square = (45 cm)^2 = 2025 cm^2
So, the value of x is 38 cm, and the area of the eighth largest square is 2025 cm^2.