Final answer:
To calculate the perimeter and area of the given rectangle, we use the perimeter formula P = 2(l + w) and the area formula A = l × w. The perimeter is 20x - 14 and the area is 24x^2 - 22x - 30.
Step-by-step explanation:
The correct answer is option Mathematics. To find the perimeter and area of a rectangle with a length of (6x-10) and a width of (4x+3), we follow these steps:
- Calculate the perimeter using the formula for the perimeter of a rectangle, P = 2(length + width). So, the perimeter P = 2[(6x - 10) + (4x + 3)].
- Simplify the expression: P = 2[6x + 4x - 10 + 3], which further simplifies to P = 2[10x - 7], and then P = 20x - 14.
- Calculate the area using the formula for the area of a rectangle, A = length × width. So, the area A = (6x - 10)(4x + 3).
- Expand the expression to find the area: A = 24x^2 + 18x - 40x - 30, which simplifies to A = 24x^2 - 22x - 30.
Therefore, the perimeter of the rectangle is 20x - 14, and the area is 24x^2 - 22x - 30.
The correct answer is option Mathematics, High School.
To find the perimeter of a rectangle, you add up all the sides. The formula for the perimeter of a rectangle is P = 2(l + w), where l represents the length and w represents the width of the rectangle.
In this case, the length of the rectangle is (6x-10) and the width is (4x+3). Therefore, the perimeter can be calculated as P = 2((6x-10) + (4x+3)) = 2(10x-7).
To find the area of a rectangle, you multiply the length by the width. The formula for the area of a rectangle is A = l * w.
In this case, the length of the rectangle is (6x-10) and the width is (4x+3). Therefore, the area can be calculated as A = (6x-10) * (4x+3) = 24x^2 - 9x - 30.