Question

Theo used a photocopier to reduce the size of the letters he wants to put on a poster. The width and the slant height of the original letter A is 12 centimeters and 16 centimeters, respectively.





Question
The slant height of the reduced letter A is 12 centimeters.



What is its width?

Answer options with 4 options
A.
6

B.
8

C.
9

D.
10

Answer 1

To solve for the width of the reduced letter A, we can use the concept of similar triangles. The original letter A has a width of 12 cm and a slant height of 16 cm. The reduced letter A has a slant height of 12 cm.

We can set up a proportion based on the dimensions of the original and reduced letters:

\[
\frac{\text{Width of reduced letter A}}{\text{Width of original letter A}} = \frac{\text{Slant height of reduced letter A}}{\text{Slant height of original letter A}}
\]

Substituting the known values:

\[
\frac{\text{Width of reduced letter A}}{12} = \frac{12}{16}
\]

Now we can cross-multiply to solve for the width of the reduced letter A:

\[
\text{Width of reduced letter A} \times 16 = 12 \times 12
\]

This simplifies to:

\[
16 \times \text{Width of reduced letter A} = 144
\]

Now, divide both sides by 16:

\[
\text{Width of reduced letter A} = \frac{144}{16} = 9
\]

Thus, the width of the reduced letter A is **9 centimeters**.

The correct answer is **C. 9**.