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The perimeter changes and doubles as well.
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How does tripling the lengths of a triangle affect its perimeter?
It triples the perimeter.
How does tripling the side lengths of a pentagon affect its perimeter?
Tripling the side lengths of a pentagon will result in tripling its perimeter. The perimeter is the sum of all the side lengths, so if each side is multiplied by three, the total perimeter also increases by the same factor. Therefore, if the original perimeter is (P), the new perimeter becomes (3P).
How does tripling the sides lengths of a triangle affect the area?
Tripling the side lengths of a triangle increases its area by a factor of nine. This is because the area of a triangle is proportional to the square of its side lengths. Therefore, if each side length is multiplied by three, the area becomes (3^2 = 9) times larger.
How does tripling the side lengths of a rectangle affect its perimeter?
Tripling the side lengths of a rectangle will triple its perimeter. The perimeter of a rectangle is calculated as ( P = 2(length + width) ). If both the length and width are multiplied by three, the new perimeter becomes ( P' = 2(3 \times length + 3 \times width) = 3 \times P ). Therefore, the perimeter increases by a factor of three.
How does doubling the side lengths of a triangle affect a perimeter?
Doubling the side lengths of a triangle results in a perimeter that is also doubled. The perimeter of a triangle is the sum of its three side lengths, so if each side length is multiplied by two, the total perimeter will similarly be multiplied by two. For example, if a triangle has side lengths of 3, 4, and 5, its original perimeter is 12, and if the side lengths are doubled to 6, 8, and 10, the new perimeter will be 24.
How does doubling the side lengths of a triangle affect its perimeter?
If the length of each side is doubled, then the perimeter is also doubled.
Why does doubling the side lengths of a right triangle affect it perimeter?
Doubling the side lengths of a right triangle increases each side by a factor of two. Since the perimeter is the sum of all three sides, the new perimeter becomes twice the original perimeter. Therefore, if you double the side lengths, the perimeter also doubles. This change maintains the triangle's shape but scales it proportionally.
Does the choice of the base affect the perimeter of a triangle?
Yes, the choice of the base can affect the perimeter of a triangle, but only if it changes the lengths of the other sides. When you select a different base while keeping the area constant, the lengths of the other sides may vary, potentially altering the perimeter. However, if the triangle's shape remains the same and only the orientation of the base is changed, the perimeter will remain unchanged.
How does doubling the side lenghts of aright triangle affect its perimeter?
Doubling the side lengths of a right triangle results in a new triangle with each side being twice as long. Since the perimeter is the sum of all the side lengths, doubling each side effectively doubles the perimeter as well. Therefore, if the original perimeter is ( P ), the new perimeter will be ( 2P ).
How does Doubling the side lengths of a figure affect its perimeter?
The perimeter is doubled.
How does doubling the side legs of a right triangle affect its perimeter?
Doubling the lengths of the two legs of a right triangle increases each leg's contribution to the perimeter. If the original leg lengths are ( a ) and ( b ), the new lengths become ( 2a ) and ( 2b ). The original perimeter is ( a + b + c ) (where ( c ) is the hypotenuse), while the new perimeter becomes ( 2a + 2b + c' ) (where ( c' ) is the new hypotenuse). Thus, the new perimeter is effectively doubled, minus any increase in the hypotenuse, leading to a perimeter that is greater than or equal to twice the original perimeter.
Why does tripling the side lengths of a right triangle affect its area?
Tripling the side lengths of a right triangle increases its area by a factor of nine. The area of a triangle is calculated using the formula ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ). When the base and height are both tripled, the new area becomes ( \frac{1}{2} \times (3 \times \text{base}) \times (3 \times \text{height}) = 9 \times \text{Area} ). Thus, the area grows by the square of the scale factor applied to the side lengths.
