Question

solve for x
x = 104
x = 153
x = 143
x = 44

Explanation:

Step1: Assume similar - shaped figures

Since the two figures seem to be similar, the ratios of corresponding sides are equal.

Step2: Set up the proportion

If we assume the ratio of the side of length 7 to the side of length 91 is the same as the ratio of the side of length 4 to the side of length \(x\). The proportion is \(\frac{7}{91}=\frac{4}{x}\).

Step3: Cross - multiply

Cross - multiplying gives us \(7x = 4\times91\).

Step4: Solve for \(x\)

First, calculate \(4\times91 = 364\). Then, \(x=\frac{364}{7}=52\). But this seems wrong as per the options. Let's assume another proportion. If we consider the ratio of the side of length 7 to the side of length 11 is the same as the ratio of the side of length 91 to the side of length \(x\). The proportion is \(\frac{7}{11}=\frac{91}{x}\).
Cross - multiply: \(7x=91\times11\).
Calculate \(91\times11 = 1001\). Then \(x = \frac{1001}{7}=143\).

Answer:

\(X = 143\)