Question

Two sides of an isosceles triangle are 10 inches and 20 inches. if the shortest side of a similar triangle is 50 inches, what is the perimeter of the larger triangle?

Answer 1

To find the perimeter of the larger triangle, we first determine the scale factor to be 5, then multiply the other sides of the smaller triangle by this scale factor, and sum all sides to get the perimeter of 250 inches.

Step-by-step explanation:

The question asks us to find the perimeter of a larger triangle that is similar to a smaller isosceles triangle with sides of 10 inches and 20 inches, given that the shortest side of the larger triangle is 50 inches.

First, we determine the scale factor by comparing the shortest side of the smaller triangle (10 inches) with the shortest side of the larger triangle (50 inches). Thus, the scale factor is 50 inches / 10 inches = 5.

Next, we apply this scale factor to the other sides of the triangle to find their lengths in the larger triangle. The other two sides of the isosceles triangle, which are equal, would be 20 inches x 5 = 100 inches each.

Finally, the perimeter of the larger triangle is the sum of all its sides, which is 50 inches + 100 inches + 100 inches = 250 inches.

Answer 2

The perimeter of any shape is equal to the sum of the length of the sides of the shape. For a triangle, it would be the sum of the three side lengths. To determine the value of the perimeter, of course, we need the length of these three. By using ratio and proportion, we would be able to determine the length of the sides assuming that the two triangles are similar. We do as follows:

10 / 20 = 50 / x

where x is the length of the longest side of the larger triangle

x = 100

So, the length of the sides of the larger triangle are 50, 50 and 100. The perimeter would be

Perimeter = 50 + 50 + 100 = 200 inches