Linda's bedroom wall has a shape of a rectangle. The length is 60 feet and the height is 9 feet when a divided the wall into two congruent triangles she plans to paint the bottom triangle blue a can of blue paint covers 12 ft.² how many cans of blue paint does Linda need for the triangular part, shade and part of her wall?
Linda needs 5 cans of blue paint for the triangular part, shade and part of her wall.
To find out how many cans of blue paint Linda needs for the triangular part, we first need to calculate the area of the triangle.
The formula to find the area of a triangle is: A = 1/2 × base × height.
The base of the triangle is the same as the length of the rectangle, which is 60 feet. The height is half of the height of the rectangle, which is 9 feet divided by 2, equal to 4.5 feet.
Now, let's calculate the area of the triangle:
A = 1/2 × 60 feet × 4.5 feet
A = 1/2 × 270 square feet
A = 135 square feet
Since one can of blue paint covers 12 square feet, we divide the area of the triangle by the coverage of one can to find out how many cans Linda needs:
Number of cans = 135 square feet / 12 square feet per can
Number of cans = 11.25 cans
Since we can't have a fraction of a can, Linda will need to round up the number of cans. Therefore, Linda needs to buy 12 cans of blue paint.
To find the area of the bottom triangle of Linda's wall, we need to use the formula for the area of a triangle: A = (1/2) * base * height.
Since the triangle is congruent to the top triangle, the base and height will be the same. Let's use 'b' to represent the base of each triangle.
The area of one triangle is given by A = (1/2) * b * 9.
To find the base, we can use the Pythagorean theorem since we know the length of the wall (60 feet) and the height of the triangle (9 feet).
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, one side is the height (9 feet), and the other side is the base (b).
Therefore, 60^2 = 9^2 + b^2.
Simplifying the equation, we have 3600 = 81 + b^2.
Subtracting 81 from both sides, we get b^2 = 3519.
Taking the square root of both sides, we find that b is approximately 59.26 feet.
Now, let's calculate the area of one triangle: A = (1/2) * 59.26 * 9 = 266.67 ft².
Since Linda wants to paint both triangles, we need to find the total area of both triangles, which is 2 * 266.67 = 533.34 ft².
Next, we need to determine how many cans of blue paint are needed to cover this area. We know that one can covers an area of 12 ft².
Dividing the total area by the area covered by one can, we get the number of cans needed: 533.34 / 12 = approximately 44.45 cans.
Therefore, Linda needs approximately 45 cans of blue paint to paint the bottom triangle, shade, and part of her wall.