The perimeter of rectangle ABCD is 256 inches. Its length is 3 times as long as its width. Find the area of triangle ABC
3W = L
2W + 2L = 256
Substitute 3W for L in second equation and solve for W. Insert that value into the first equation and solve for L. Check by inserting both values into the second equation.
L * W = ?
To find the area of triangle ABC, we first need to determine the dimensions of the triangle. Since the rectangle has a length that is three times its width, let's assign a variable to the width of the rectangle.
Let's say the width of the rectangle is 'w' inches.
Therefore, the length of the rectangle would be three times the width: 3w inches.
Now, let's find the perimeter of the rectangle. The perimeter of a rectangle can be calculated by adding the lengths of all four sides. Given that the perimeter is 256 inches, we can set up the following equation:
2w + 2(3w) = 256
Simplifying the equation, we get:
2w + 6w = 256
8w = 256
w = 32
Now that we know the width of the rectangle is 32 inches, we can find the length:
Length = 3w = 3 * 32 = 96 inches
So, the dimensions of the rectangle ABCD are: width = 32 inches and length = 96 inches.
Finally, let's find the area of triangle ABC. The area of a triangle can be calculated using the formula: area = (base * height) / 2.
In this case, the base of triangle ABC would be the width of the rectangle, which we found to be 32 inches. The height of triangle ABC would be the length of the rectangle, which we found to be 96 inches.
Plugging in the values into the formula, we get:
Area of triangle ABC = (32 * 96) / 2
= 3072 square inches
Therefore, the area of triangle ABC is 3072 square inches.