Question

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?

I don't know where to begin...

Answer 1

Since the shapes are similar, the ratio of their corresponding sides must be the same

so....

new side/24 = newbase/oldbase
newside/24 = 11/16
newside = 11(24)/16 = 16.5 mm

check:
newside/oldside = 16.5/24 =.6875
newbase/oldbase = 11/16 = .6875
we're good!

Answer 2

16.5