Question

solve for x. the triangles are similar. a) 10 b) 8 c) 5 d) 4

Explanation:

Step1: Use the property of similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{60}{84}=\frac{55}{9x + 5}\)

Step2: Cross - multiply

Cross - multiplying gives \(60\times(9x + 5)=55\times84\)

Step3: Expand the left - hand side

\(60\times9x+60\times5 = 55\times84\), which is \(540x+300=4620\)

Step4: Isolate the term with \(x\)

Subtract \(300\) from both sides: \(540x=4620 - 300\), so \(540x=4320\)

Step5: Solve for \(x\)

Divide both sides by \(540\): \(x=\frac{4320}{540}\)

Answer:

\(x = 8\), so the answer is B. Option Text