The frame of a picture is 30 cm by 36 cm outside. If the area of the picture (inner rectangle) is 480 square cm, what is the width of the uniform border?
let the border be x cm wide
picture is (30-2x) by (36-2x)
(30-2x)(36-2x) = 480
1080 - 132x + 4x^2 - 480 = 0
4x^2 - 132x + 600 = 0
x^2 - 33x + 150 = 0
solve using the quadratic equation,
To find the width of the uniform border, we need to subtract the area of the picture (inner rectangle) from the area of the frame (outer rectangle).
Step 1: Calculate the area of the frame (outer rectangle).
The frame is given to be 30 cm by 36 cm outside.
Area of the frame = Length × Width = 30 cm × 36 cm.
Step 2: Calculate the area of the picture (inner rectangle).
The area of the picture is given to be 480 square cm.
Step 3: Subtract the area of the picture from the area of the frame.
Border area = Area of the frame - Area of the picture.
Now let's perform the calculations to find the width of the uniform border:
Area of the frame = 30 cm × 36 cm = 1080 square cm.
Border area = 1080 square cm - 480 square cm.
Border area is the area of the uniform border on all four sides of the picture.
Step 4: Divide the border area by the length (or width) of the frame.
Since the border is uniform on all four sides of the picture, divide the border area by the length or width of the frame.
Assuming we are finding the width of the uniform border, let's divide the border area by the width of the frame.
Width of the border = Border area ÷ width of the frame.
Now let's substitute the values and calculate the width of the uniform border:
Border area = 600 square cm (1080 square cm - 480 square cm).
Width of the frame = 36 cm (given).
Width of the border = 600 square cm ÷ 36 cm.
Using a calculator, we get:
Width of the border ≈ 16.67 cm (rounded to two decimal places).
Therefore, the width of the uniform border is approximately 16.67 cm.