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?
the lenth of the equal side of new pair of rings are 10.5 mm
10.5 mm
To find the length of the equal-length sides of the new pair of earrings, we need to use the concept of similarity between geometric shapes.
In the original pair of earrings, we have an isosceles triangle with equal side lengths of 24 mm and a base length of 16 mm.
In the new pair of earrings, we are given that the base length is 11 mm. We need to determine the length of the equal-length sides.
Since the two pairs of earrings are similar in shape, their corresponding sides are proportional. This means that the ratio of the length of the equal-length sides in the original pair of earrings to the length of the equal-length sides in the new pair of earrings will be the same as the ratio of the base lengths.
Let's represent the length of the equal-length sides in the new pair of earrings as "x".
The ratio can be set up as follows:
(24 mm) / (x) = (16 mm) / (11 mm)
To solve for "x", we cross-multiply and solve the resulting equation:
(24 mm) * (11 mm) = (16 mm) * (x)
264 mm^2 = 16x mm
To isolate "x", we divide both sides of the equation by 16 mm:
264 mm^2 / 16 mm = x
16.5 mm = x
Therefore, the length of the equal-length sides of the new pair of earrings is 16.5 mm.