Include the LET statement for the equation below:

An art dealer advises that, for the best display of a painting, the area of the frame should be 1/5 the area of the painting. Determine the best width of the frame for a painting 20-cm by 20-cm, if the width is to be the same on all sides. Round you answer to the nearest tenth.

let w equal the width of the frame

the frame is made up of four pieces ... 20+w long, and w wide

4 * w * (20 + w) = 20 * 20 / 5 ... 80 w + 4 w^2 = 80 ... w^2 + 20 w - 20 = 0

use the quadratic formula to find w

To find the best width of the frame for a painting, we can use the formula:

Frame Area = (1/5) * Painting Area

First, let's calculate the area of the painting. The painting is a square with side length 20 cm, so the area of the painting is:

Painting Area = Side Length * Side Length = 20 cm * 20 cm

Next, let's substitute this into the formula for frame area:

Frame Area = (1/5) * (20 cm * 20 cm)

Finally, let's find the width of the frame by taking the square root of the frame area (since the frame is square and all sides are the same):

Width of Frame = √(Frame Area)

Rounding the answer to the nearest tenth, we can now write the LET statement:

LET Frame_Area = (1/5) * (20 cm * 20 cm)
LET Width_of_Frame = √(Frame_Area)

To determine the best width of the frame for a painting, we can use a LET statement to represent the width of the frame. Let's say the width of the frame is represented by the variable "x" (in cm).

The given information states that the area of the frame should be 1/5 the area of the painting. The area of the painting can be calculated by multiplying its length by its width. In this case, both the length and width of the painting are 20 cm. Therefore, the area of the painting is 20 cm * 20 cm = 400 cm^2.

According to the advice, the area of the frame should be 1/5 times the area of the painting. So, the area of the frame can be calculated as (1/5) * 400 cm^2 = 80 cm^2.

Now, we can determine the dimensions of the frame using the area. Since the frame is rectangular and the width is the same on all sides, we can set up the equation:

Area of the frame = (length of the frame) * (width of the frame)

Substituting the values we have:

80 cm^2 = (20 cm + 2x) * x

Simplifying further:

80 cm^2 = (20 cm * x) + (2 * x^2)

This is a quadratic equation, and we can solve it to find the width of the frame (x). By rearranging the equation and setting it equal to zero, we get:

2 * x^2 + 20 * x - 80 = 0

Now, you can use any appropriate method, such as factoring or the quadratic formula, to solve for x. Once you find the value of x, you can round it to the nearest tenth to get the best width of the frame for the given painting.