Question

Given ΔDEF : ΔRST, find the scale factor.

Answer 1

the answer is twelve

Answer 2

Answer: The value of x is 12 units and the scale factor is
`(4)/(3).`

Step-by-step explanation: Given that the triangle DEF is similar to the triangle RST.

We are to find the value of x and the scale factor of the dilation.

We know that the corresponding sides of the similar triangles are proportional.

So, we must have

`(DE)/(RS)=(EF)/(ST)\\\\\\\Rightarrow (3)/(x)=(4)/(16)\\\\\\\Rightarrow (3)/(x)=(1)/(4)\\\\\Rightarrow x=3*4\\\\\Rightarrow x=12.`

The scale factor is given by

`S=\frac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}\\\\\\\Rightarrow S=(RS)/(DE)\\\\\\\Rightarrow S=(4)/(3).`

Thus, the value of x is 12 units and the scale factor is
`(4)/(3).`