A triangle has sides of lengths 3.2. 5.7, and 7.2 inches. The smallest side of a similar triangle is 1.4 inches. What are the lengths of the other two sides? Write the smaller side length first and the larger side length second
The smaller side length is ___ inches and the larger side length is ___ inches
To find the lengths of the other two sides, we need to find the scale factor. The scale factor is found by dividing the length of the corresponding sides of the two triangles.
Let x be the scale factor.
According to the information given,
3.2 / 1.4 = 5.7 / x
Cross-multiplying and solving for x, we get:
3.2 * x = 1.4 * 5.7
3.2x = 7.98
x = 7.98 / 3.2
x ≈ 2.49375
Now we can find the lengths of the other two sides:
The length of the smaller side of the similar triangle is 1.4 inches.
The length of the larger side can be found by multiplying the length of the corresponding side in the original triangle by the scale factor:
5.7 * 2.49375 ≈ 14.2125 inches
Therefore, the lengths of the other two sides are approximately:
The smaller side length is 1.4 inches and the larger side length is 14.2125 inches.
A rectangle on a coordinate plane has a length of 5 units and a width of 3 units. If the rectangle is dilated by a scale factor of 5, what is its new area?
The new area of a shape after dilation is equal to the scale factor squared times the original area.
The original area of the rectangle is length times width:
Area = Length * Width = 5 * 3 = 15 square units
To find the new area after a dilation with a scale factor of 5:
New Area = Scale Factor^2 * Original Area = 5^2 * 15 = 25 * 15 = 375 square units
Therefore, the new area of the rectangle after dilation is 375 square units.
A triangle on a coordinate plane was dilated. After being dilated, its area is 6.25 times as great as the original figure. What is the scale factor?
Let's assume the scale factor is represented by the variable x.
The area of a triangle is given by the formula:
Area = (1/2) * base * height
If the original area of the triangle is A, then the new area after dilation will be 6.25 * A.
According to the formula for area, we have:
6.25 * A = (1/2) * x * base * x * height
Simplifying the equation gives:
6.25 * A = (x^2) * (1/2) * base * height
Dividing both sides of the equation by (1/2) * base * height:
12.5 * A = (x^2)
Now let's find the square root of both sides:
sqrt(12.5 * A) = x
Therefore, the scale factor x is equal to the square root of (12.5 * A).