The sides of a triangle have lengths of 9, 11, and 16 units. What is the perimeter of a similar triangle with its longest side 24 units in length?
since 24/16 = 3/2, the perimeter will be 3/2 as big. All the sides are 3/2 as big.
54
Well, if we're talking about similar triangles, then we're going to need some similar jokes! Let's dive in, shall we?
To find the perimeter of the similar triangle, we need to scale up the sides by the same factor. So, if we want to go from a longest side of 16 units to 24 units, that's a scaling factor of 24/16 = 1.5.
Now, let's calculate the new side lengths of the similar triangle using this scaling factor. The first side would be 9 * 1.5 = 13.5 units, the second side would be 11 * 1.5 = 16.5 units, and the longest side would be 24 units.
Finally, let's add up all the side lengths to get the perimeter. So, the perimeter of the similar triangle would be 13.5 + 16.5 + 24 = 54 units.
Now that's a similar joke! I mean, a similar triangle. Ha!
To find the perimeter of a similar triangle, we need to determine the scale factor between the two triangles. The scale factor is the ratio of the corresponding sides in the two triangles.
First, let's find the scale factor for the longest sides. The longest side in the original triangle is 16 units, and the longest side in the new similar triangle is 24 units. The scale factor for the longest sides is therefore 24/16 = 3/2.
Next, we can find the scale factors for the other two sides by multiplying the scale factor for the longest sides by the ratios of the corresponding sides in the original triangle.
For the side with length 9 units, the corresponding side in the new triangle will have a length of (3/2) * 9 = 13.5 units.
For the side with length 11 units, the corresponding side in the new triangle will have a length of (3/2) * 11 = 16.5 units.
Finally, we can calculate the perimeter of the new similar triangle by adding up the lengths of all three sides:
Perimeter = 13.5 + 16.5 + 24 = 54 units.
Therefore, the perimeter of the similar triangle with its longest side 24 units in length is 54 units.
To find the perimeter of a similar triangle, we need to understand the concept of similarity in triangles. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
In this case, we have a triangle with side lengths of 9, 11, and 16 units and we need to find the perimeter of a similar triangle with its longest side of 24 units.
First, let's determine the scale factor between the two triangles. The scale factor is the ratio of the corresponding side lengths in the two triangles.
In the original triangle, the longest side is 16 units. In the similar triangle, the longest side is 24 units. So, the scale factor is 24/16 = 3/2.
Next, we need to apply the scale factor to all the side lengths of the original triangle to find the corresponding side lengths in the similar triangle.
For the original triangle, the sides are 9, 11, and 16 units. Multiplying each side by the scale factor of 3/2, we get:
Side 1: 9 * 3/2 = 13.5 units
Side 2: 11 * 3/2 = 16.5 units
Side 3: 16 * 3/2 = 24 units
Now we have the side lengths of the similar triangle: 13.5, 16.5, and 24 units.
Finally, we can calculate the perimeter of the similar triangle by adding up all the side lengths:
Perimeter = 13.5 + 16.5 + 24 = 54 units
Therefore, the perimeter of the similar triangle with its longest side of 24 units is 54 units.