A triangle was dilated by a scale factor of 2. If cos [tex]a ^{\circ}=\frac{3}{5}[/tex] and [tex]\overline{ FD }[/tex] measures 6 units, how long is [tex]\overline{ DE }[/tex]?
Answer (1)
The triangle is dilated by a scale factor of 2, meaning each side is twice as long.
F D measures 5 units.
Calculate the length of D E using the scale factor: D E = 2 × F D = 2 × 5 = 10 .
The length of D E is 10 units.
Explanation
Analyze the problem and given data We are given that a triangle is dilated by a scale factor of 2. This means that every side of the triangle is multiplied by 2. We are also given that F D measures 5 units. We want to find the length of D E , which corresponds to F D after the dilation. The information about cos a ∘ = 5 3 is irrelevant to the problem.
Determine the relationship between DE and FD Since the triangle is dilated by a scale factor of 2, the length of D E is twice the length of F D . Therefore, we have:
Calculate the length of DE D E = 2 × F D We are given that F D = 5 units. Substituting this value into the equation, we get: D E = 2 × 5 = 10 Therefore, the length of D E is 10 units.
State the final answer The length of D E is 10 units.
Examples
Imagine you are drawing a map. You start with a small sketch, and then you want to enlarge it to a bigger poster. If you use a scale factor of 2, it means every distance on the poster will be twice as long as the corresponding distance on your sketch. So, if a road is 5 cm long on your sketch, it will be 10 cm long on the poster.
