Question

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

Answer 1

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.

Answer 2

x = 5/3, or 1 2/3

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)