An artist is working on a painting that is 3 inches longer than it is wide. The area of the painting is 154 square inches what is the length of the painting?
w(w+3) = 154
11*14 = 154
To find the length of the painting, we need to first set up an equation using the given information.
Let's assume that the width of the painting is "x" inches.
According to the given information, the length of the painting is 3 inches longer than its width. So, the length can be represented as "x + 3" inches.
The area of a rectangle is found by multiplying its length and width. In this case, we know that the area is 154 square inches. So, we have the equation:
Area = Length × Width
154 = (x + 3) × x
To solve the equation, we can distribute the x, which gives us:
154 = x^2 + 3x
Rearranging the equation to form a quadratic equation:
x^2 + 3x - 154 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, I'll use factoring.
By factoring, we need to find two numbers whose sum is 3 and whose product is -154. After evaluating the possible pairs, we find that the numbers are 11 and -14.
So, we can rewrite the equation as:
(x + 11)(x - 14) = 0
Now we can solve for x by setting each factor equal to zero:
x + 11 = 0 or x - 14 = 0
Solving for x, we get:
x = -11 or x = 14
Since the width of the painting cannot be negative, we discard the -11. Therefore, the width of the painting is 14 inches.
Now, to find the length, we add 3 to the width:
Length = Width + 3
Length = 14 + 3
Length = 17 inches
So, the length of the painting is 17 inches.
Let's start by assigning a variable to represent the width of the painting. Let's say the width is "x" inches.
Since the length of the painting is 3 inches longer than the width, we can say the length is "x + 3" inches.
The area of a rectangle is equal to the length multiplied by the width. In this case, the area is given as 154 square inches, so we can set up the equation:
Length * Width = Area
(x + 3) * x = 154
Next, we can simplify the equation by multiplying the terms:
x^2 + 3x = 154
Rearranging the equation to set it equal to zero:
x^2 + 3x - 154 = 0
Now we can solve this quadratic equation. Factoring or using the quadratic formula will help us find the solutions.