you trim a large square picture so that you could fit it into a frame. you trim 3 inches from the length and 2 inches from the width. the area of the resulting picture is 56sq in what was the perimeter of the original large square picture?
So you actually have to use the Pythagoras theorem. The use of imaginary number divided by the contagion of 71. Professor at Langster College.
Let the original square be x by x inches
after trimming,
the length is x-4 and the width is x-6
area = (x-4)(x-6) = 56
x^2 - 10x + 24 = 56
x^2 - 10x + 25 = 56-24 + 25
(x-5)^2 = 57
x-5 = ±√57
x = 5 +√57 or a negative
perimeter of original square = 4(5+√57) = appr 50.2 inches
To find the perimeter of the original large square picture, we need to determine the length and width of the trimmed picture and then calculate the perimeter using those dimensions.
Let's assume the original dimensions of the large square picture are represented by "x". Therefore, the length of the trimmed picture would be (x - 3) inches, and the width would be (x - 2) inches.
The area of the resulting picture is given as 56 square inches, so we can set up the equation:
Area = Length * Width
56 = (x - 3) * (x - 2)
Now, we can solve this quadratic equation to find the value of x:
56 = x^2 - 5x + 6
x^2 - 5x + 6 - 56 = 0
x^2 - 5x - 50 = 0
To solve the quadratic equation, we can either factor it or use the quadratic formula. In this case, it is easier to factor:
(x - 10)(x + 5) = 0
Setting each factor equal to zero, we get:
x - 10 = 0 or x + 5 = 0
x = 10 or x = -5
Since we are dealing with dimensions, a negative value does not make sense. Therefore, we discard x = -5 and conclude that the original dimension of the large square picture is x = 10 inches.
Now that we have the dimension of the original large square picture, we can calculate its perimeter:
Perimeter = 4 * Length
Perimeter = 4 * 10 inches
Perimeter = 40 inches
So, the perimeter of the original large square picture is 40 inches.