a square painting is surrounded by a 2.5cm frame. if the total are of the painting plus frame is 3600 sq cm, find the dimensions of the painting.
what are the dimensions? i forgot how to find the dimensions. please help me .
Since the painting is square, the length of each side of the painting, a, is such that
(a + 5)^2 = 3600 cm^2
a + 5 = 60 cm
a = 55 cm
The "5" in that equation is the width of two frame borders that must be added to the painting dimension
what's ^2 ? :)
could you do it in a RESC form?
No to the RESC form, whatever that is.
The logic of the method should be apparent.
^2 means "squared". The ^ in front of the 2 means that the 2 is an exponent.
representation, equation, solution and conclusion.
is that true? the answer, how old are you two?
To find the dimensions of the painting, we need to consider the dimensions of both the painting and the frame. Let's denote the length of one side of the painting as "x" cm.
The length of one side of the entire square (including the frame) is then equal to "x + 2.5" cm, as each side of the painting is surrounded by a 2.5 cm frame.
The area of the entire square (including the frame) is given as 3600 sq cm. Since the shape is a square, we know that the length and width are equal. Therefore, we can use the formula for the area of a square: Area = side * side = side^2.
So, the equation becomes:
(x + 2.5) * (x + 2.5) = 3600
To solve this equation, we can expand the equation and then solve for x.
x^2 + 5x + 6.25 = 3600
Rearranging the equation:
x^2 + 5x - 3593.75 = 0
Now, we can solve this quadratic equation using any suitable method, such as factoring, completing the square, or using the quadratic formula.
By solving the quadratic equation, we find that the value of x is approximately 58.6 cm (rounded to one decimal place).
Therefore, the dimensions of the painting are approximately 58.6 cm by 58.6 cm.