Question

10 if $\triangle qrs\sim\triangle tuv$, find the value of x.
a $x = 12$
b $x = 41$
c $x = 20$
d $x = 11$

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle QRS\sim\triangle TUV\), the ratios of corresponding sides are equal. That is \(\frac{QR}{TU}=\frac{RS}{UV}\).

Step2: Substitute the given values

We have \(QR = 24\), \(TU=x + 5\), \(RS = 54\), \(UV=36\). Substituting into the ratio \(\frac{24}{x + 5}=\frac{54}{36}\).

Step3: Cross - multiply

Cross - multiplying gives \(24\times36=54\times(x + 5)\).

Step4: Simplify the equation

\(864 = 54x+270\).

Step5: Solve for \(x\)

Subtract \(270\) from both sides: \(864-270 = 54x\), so \(594 = 54x\). Then \(x=\frac{594}{54}=11\).

Answer:

D. \(x = 11\)