If the sides of a square are increased by 3m, the area becomes 64m2. Find the length of a side of the original square.
A 4 m by 6 m rug covers half of the floor area of a room and leaves a uniform strip of bare floor around the edges. What are the dimensions of the room?
How about showing me what you got so far?
(X + 3)(X + 3) = 64
4 * 6 = .5X
For each problem, solve for X.
However, that only gives the floor area. There is no information about ceiling height.
I hope this helps. thanks for asking.
To solve the first problem, we need to find the length of a side of the original square. Let's assume the length of a side of the original square is "x" meters.
According to the problem, if the sides of the square are increased by 3 meters, we need to add 3 meters to both dimensions. This means the length of a side of the new square is (x + 3) meters.
The area of a square is calculated by squaring the length of its side. Hence, the area of the original square is x^2 square meters, and the area of the new square is (x + 3)^2 square meters.
The problem gives us the information that the area of the new square is 64 square meters. Therefore, we can write the equation:
(x + 3)^2 = 64
Now, let's solve this equation to find the length of a side of the original square.
Taking the square root of both sides of the equation, we get:
x + 3 = √64
Simplifying the square root:
x + 3 = 8
Subtracting 3 from both sides:
x = 8 - 3
x = 5
So, the length of a side of the original square is 5 meters.
To solve the second problem, we need to find the dimensions of the room using the given information about the rug.
Let's assume the length of the room is L meters and the width is W meters.
According to the problem, the rug covers half of the floor area of the room. This means the area of the rug is equal to half the area of the room.
The area of a rectangular rug is calculated by multiplying its length by its width. Hence, the area of the rug is L * W square meters.
Since the rug covers half of the floor area, we have:
L * W = (1/2) * (L * W) * 2
Simplifying this equation, we get:
L * W = (1/2) * L * W * 2
Canceling out common terms, we have:
1 = 1/2 * 2
This equation is true, meaning the dimensions of the room can be any positive numbers.
Therefore, the dimensions of the room cannot be determined with the given information.