mang pedring wanted to construct a square table such that the length of its side is 30 cm longer than its height.
Suppose the area of the table is 2.25m^2, what would be its height?
*I had a correction for the last question you posted:
Q: mang pedring wanted to construct a square table such that the length of its side is 30 cm longer than its height.
What expression represents the area of the table? Suppose the table is 90 cm high what would be the area?
A:
Let x = height of table
Let x+30 = length of table
Recall that area of square is given by
A = L^2
where L = length of one side.
substituting,
A = (x+30)^2
A = x^2 + 60x + 900
If table is 90 cm high, then the length of square is 120 cm. Substituting this to the equation for area,
A = 90^2 + 60(90) + 900
A = 14400 cm^2
*sorry about that! The x value substituted must be 90, not 120.
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~for the current question,
Let x = height of the table
let x + 30 = length of table
recall that area of a square is given by
A = L^2
where L = length of one side of square
substituting,
2.25 = L^2
L = sqrt(2.25)
L = 1.5 m
note that 30 cm = 0.3 m, thus,
1.5 = x + 0.3
x = 1.2 m (height)
hope this helps~ :D
lots of THANK YOU! maraming salamat! :D
To solve this problem, we first need to find the dimensions of the square table by setting up an equation based on the given information.
Let's represent the height of the table as "h" (in cm). Since the length of its side is 30 cm longer than its height, the length can be represented as "h + 30" (in cm).
The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side. In this case, the area is given as 2.25 m^2, which is equivalent to 22500 cm^2.
So, our equation becomes: (h + 30)^2 = 22500
To find the height, we need to solve this equation. Here's how you can do it step-by-step:
1. Expand the square: h^2 + 60h + 900 = 22500
2. Move 22500 to the left side of the equation: h^2 + 60h + 900 - 22500 = 0
3. Simplify: h^2 + 60h - 21600 = 0
Now, we have a quadratic equation. We can either factor it or use the quadratic formula.
If we factor it, we would get: (h - 120)(h + 180) = 0
From here, we have two possible solutions:
- h - 120 = 0, which gives us h = 120 (reject this solution because the height cannot be negative)
- h + 180 = 0, which gives us h = -180 (reject this solution as well)
Therefore, the height of the square table would be 120 cm.