Question

Robert made a design on his wall with the similar pentagon tiles shown. L R 9 cm 9 cm M K S 15 cm 10 cm 10 cm 15 cm U 10 cm T P 15 cm N * not drawn to scale What is the length of side RS?

Answer 1

Answer:

RS = 6 cm

Explanation:

If the pentagons are similar, the ratio of their sides is constant. So, we can use the following equation to calculate the length of RS:

$\frac{MN}{ST}=\frac{LM}{RS}$

Then, we can replace the value of MN by 15 cm, LM by 9 cm, and ST by 10 cm:

$\frac{15}{10}=\frac{9}{RS}$

Now, we can solve the equation for RS as:

$\begin{gathered} 1.5=\frac{9}{RS} \\ 1.5RS=\frac{9}{RS}\cdot RS \\ 1.5RS=9_{} \\ \frac{1.5RS}{1.5}=\frac{9}{1.5} \\ RS=6 \end{gathered}$

Therefore, the length of the side RS is 6 cm