A 5cm piece of wire is cut into two parts such that a square formed by bending on part will have four times the area of a square formed by bending the other part, what is the length of the longer part.
I just don't know what the equation would look like.
4 times the area means 2 times the side length. So, if x is the smaller side,
4x + 4(2x) = 5
To solve this problem, let's assume that the length of the shorter part of the wire is x cm.
We're given that the longer part of the wire, which we'll represent as (5 - x) cm, forms a square with four times the area of the square formed by the shorter part.
To find the area of a square, we square the length of one side. Therefore, the area of the square formed by the shorter part is x^2 square cm.
According to the problem, the longer part forms a square with four times the area of the shorter part. So the area of the square formed by the longer part is 4x^2 square cm.
Since the total length of the wire is 5 cm, we can write the equation:
x + (5 - x) = 5
Simplifying this equation, we get:
2x = 5
x = 5/2
Therefore, we find that x is 2.5 cm.
To determine the length of the longer part, we substitute the value of x back into our equation:
5 - 2.5 = 2.5
So the longer part of the wire is 2.5 cm.