if the lengths of the sides of one triangle are 2 inches 5 inches and 7 inches respectively in the shortest leg of a similar triangle is 4 inches what is the perimeter of the second triangle in inches?
sorry - no triangle has sides of 2,5,7. That is just a straight line of length 7.
Whoever devised this problem was sadly unaware of properties of a triangle.
Anyway, supposing you have a real triangle, if the sides are doubled, so is the perimeter.
Find the perimeter and area of the figure
12inches and 5inches
To find the perimeter of the second triangle, we need to determine the ratio of corresponding sides between the two triangles since they are similar.
In the first triangle, the shortest leg is 2 inches. In the second triangle, the shortest leg is 4 inches. To find the ratio between the corresponding sides, we divide the side lengths of the second triangle by the side lengths of the first triangle, in this case:
Ratio = (Shortest leg of the second triangle) / (Shortest leg of the first triangle)
Ratio = 4 inches / 2 inches
Ratio = 2
Now that we have the ratio, we can use it to find the lengths of the other sides of the second triangle.
For the second triangle, the ratio also applies to the other sides. So, the other sides of the second triangle would be:
- The second leg: 5 inches * 2 = 10 inches
- The third leg: 7 inches * 2 = 14 inches
Now, to find the perimeter of the second triangle, we add up all the side lengths:
Perimeter = Shortest leg + Second leg + Third leg
Perimeter = 4 inches + 10 inches + 14 inches
Perimeter = 28 inches
Therefore, the perimeter of the second triangle is 28 inches.