Question

9 given the two triangles are similar, solve for the value of x. δabc ~ δdef a 77 b 11x + 11 c d 21 e 30 f a x = 11 b x = 9 c x = 9.18 d x = 7.18

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{BC}{EF}\). Here \(AB = 77\), \(DE=21\), \(BC = 11x + 11\), \(EF = 30\). So we have the proportion \(\frac{77}{21}=\frac{11x + 11}{30}\).

Step2: Simplify the left - hand side of the proportion

Simplify \(\frac{77}{21}\), divide both numerator and denominator by \(7\), we get \(\frac{77\div7}{21\div7}=\frac{11}{3}\). So the proportion becomes \(\frac{11}{3}=\frac{11x + 11}{30}\).

Step3: Cross - multiply

Cross - multiplying gives \(11\times30=3\times(11x + 11)\).

Step4: Expand the right - hand side

Expand \(3\times(11x + 11)\) to get \(33x+33\). So \(330 = 33x+33\).

Step5: Solve for \(x\)

Subtract \(33\) from both sides: \(330-33=33x\), which is \(297 = 33x\). Then divide both sides by \(33\), \(x=\frac{297}{33}=9\).

Answer:

B. \(x = 9\)