Question

Solve of x. A. 1 2/3 B. 2 2/5 C. 2/3 D. 5/12​

Answer 1

Answer:

x = 5/3, or 1 2/3

Step-by-step explanation:

These two triangles are similar because the acute angle is the same in both cases.  Thus,

the ratio of hypotenuse 2 to hypotenuse 12 is equal to x/10:

  2         x

------- = ------

 12        10

                                                                                             20

Cross multiplying, we get 12x = 20.  Solving for x:  x = ---------- =  5/3

                                                                                              12

x = 5/3, or 1 2/3  (Answer A)

Answer 2

Solution:

Since the image is larger than the pre-image, the scale factor will be 6. This means that the pre-image is 6 times smaller than the image. We can also put this in ratio form.

• Pre-image hypotenuse: 2
• image hypotenuse: 12
• => 12:2 = 6

Let's do the same thing with x and 10, as they are corresponding sides.

• Pre-image leg₁: x
• Image leg₂: 10
• => 10/x = 6

Solve for x.

• 10/x = 6
• => 10 = 6(x)
• => x = 10/6 = 5/3
• 5/3 = 1 2/3

Option A is correct.