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...
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!
16.5
To find the length of the equal-length sides of the new pair of earrings, we can use the concept of similar triangles.
First, let's understand the relationship between the original pair of earrings and the new pair.
The original pair of earrings is in the shape of an isosceles triangle, which means it has two equal-length sides and one base. The equal-length sides are 24 mm and the base length is 16 mm.
Now, Davida uses one earring to make another pair of earrings similar in shape to the original pair, but with a different base length of 11 mm.
Since the triangles are similar, the corresponding sides of the triangles are proportional. This means we can create a ratio of the corresponding side lengths:
(original equal-length side length) / (original base length) = (new equal-length side length) / (new base length)
Substituting the given values, we have:
24 mm / 16 mm = (new equal-length side length) / 11 mm
Now, we can solve for the length of the equal-length sides of the new pair of earrings.
Cross-multiplying the equation:
(24 mm)(11 mm) = (16 mm)(new equal-length side length)
264 mm^2 = 16 mm * (new equal-length side length)
Dividing both sides by 16 mm:
(264 mm^2) / 16 mm = new equal-length side length
By simplifying the left side:
16.5 mm = new equal-length side length
So, the length of the equal-length sides of the new pair of earrings is 16.5 mm.