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A rectangle with a perimeter of 30 centimeters is twice as long as it is wide. What is the area of the rectangle in square centimeters?
The area of the rectangle is 50 square centimeters.
Let’s denote the width of the rectangle as “w” centimeters. Since the length is twice the width, the length would be “2w” centimeters.
Given that the perimeter of the rectangle is 30 centimeters, we can set up an equation:
Perimeter = 2 × (length + width)
So, 30 = 2 × (2w + w)
30 = 2 × 3w
30 = 6w
Now, solve for “w”:
w = 30/6
w = 5
Now that we’ve found the width, we can find the length:
Length = 2w = 2 × 5 = 10 centimeters
Now, the area of the rectangle is:
Area = Length × Width
Area = 10 × 5 = 50 square centimeters
So, the area of the rectangle is 50 square centimeters.
Formulas for Finding Area and Perimeter of a Triangle
There are different formulas depending on what information you have about the triangle:
Perimeter:
The perimeter of a triangle is simply the sum of the lengths of all three sides.
Formula: Perimeter = a + b + c
where a, b, and c are the lengths of the sides.
Area:
There are several formulas for finding the area of a triangle, depending on what information you have:
General Formula:
Formula: Area = 1/2 * base * height
where “base” is the length of any side of the triangle and “height” is the perpendicular distance from that base to the opposite vertex.
Other Formulas:
- If you know all three side lengths:
- Heron’s Formula: Area = √(s(s – a)(s – b)(s – c)) where s is the semi-perimeter (half the perimeter) and a, b, and c are the side lengths.
- If you know two sides and the included angle:
- Area = 1/2 * side 1 * side 2 * sin(θ) where θ is the angle between the two sides.
Special Cases:
- Equilateral Triangle:
- Perimeter = 3 * side length
- Area = √3 / 4 * side length^2
- Right Triangle:
- Perimeter = a + b + c (where c is the hypotenuse)
- Area = 1/2 * base * height (where the base and height are the two shorter sides)
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Source: Math Hello Kitty
Categories: Math
