Davida bought a pair of earrings, each in the shape of an isosceles triangle with equal side lengths of 24 mm and a base length of 16 mm. She used one earring to make another pair of earrings, similar in shape, with the base length equal to 11 mm.
What is the length of the equal-length sides of this new pair of earrings?
11/16 = x/24
Solve for x.
To find the length of the equal-length sides of the new pair of earrings, we can use the concept of similar triangles.
In the original pair of earrings, we have an isosceles triangle with two equal sides measuring 24 mm each and a base length of 16 mm. Let's call these sides "a" and the base length "b".
Now, in the new pair of earrings, we are given that the base length is 11 mm. Let's call the length of the equal sides of the new triangle "x".
Since the new pair of earrings is similar in shape to the original pair, we can set up a proportion based on the ratios of corresponding side lengths:
a / b = x / 11
Using the original pair of earrings, we know that a = 24 mm and b = 16 mm. Plugging in these values, we get:
24 / 16 = x / 11
Simplifying the proportion:
1.5 = x / 11
To solve for x, we can cross-multiply:
1.5 * 11 = x
x = 16.5
Therefore, the length of the equal-length sides of the new pair of earrings is 16.5 mm.