Question

pentagon m is a scaled copy of pentagon l.
pentagon l has sides labeled ( 3\frac{1}{3} ), ( 5 ), ( 1\frac{1}{2} ). pentagon m has sides labeled ( 2\frac{1}{2} ), ( n ), ( 1\frac{1}{8} ).
what is the value of ( n )?

Explanation:

Step1: Convert mixed numbers to improper fractions

\(3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3}\), \(2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}\), \(1\frac{1}{2}=\frac{3}{2}\), \(1\frac{1}{8}=\frac{9}{8}\)
Since pentagon \(M\) is a scaled - copy of pentagon \(L\), the ratios of corresponding sides are equal. Let the scale factor be \(k\). Then \(k=\frac{\text{side of }M}{\text{side of }L}\)
We can use the pair of known corresponding sides: \(\frac{2\frac{1}{2}}{3\frac{1}{3}}=\frac{\frac{5}{2}}{\frac{10}{3}}=\frac{5}{2}\times\frac{3}{10}=\frac{3}{4}\)

Step2: Use the scale factor to find \(n\)

We know that \(\frac{n}{5}=\frac{3}{4}\) (because the ratio of corresponding sides is the scale factor). Cross - multiply: \(4n = 5\times3\)
\(4n=15\), then \(n=\frac{15}{4}=3.75\)

Answer:

\(3.75\)