Question

Question 10 of 10 6 st Answer here 5 E Given the two similar triangles above, what is the measure of side DE?​

Answer 1

DE = 3

Explanation:

What is a scale factor?

A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of
`(1)/(2)` means that the new shape is half the size of the original.

To solve for a missing length, we can use this expression:

• 
  `a^(2) +b^(2) =c^(2)`

Inserting our numbers into the expression:

• 
  `8^(2)+ b^(2) =10^(2)`
• 
  `64 + b^(2) = 100`

Subtract 64 from each side:

• 
  `(64 - 64) + b^(2) =(100-64)`
• 
  `b^(2) =36`
• 
  `√(36) =6`

Therefore, the missing side length is 6.

Looking at the side CB, it is 10 units long. If the new shape is 5 units long, that means that the scale factor from shape 1 to 2 is
`(1)/(2)`, meaning it is half its size. If the new shape is half its size, we can use this expression to solve for the missing length:

• 6 ×
  `(1)/(2)` or 6 ÷ 2 = 3

Therefore, the measure of DE is 3.