Question
In the given figure, given that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and quad ABCD ∼ quad PQRS. Determine the value of x, y, z in each case.
✓
Answer
- We have, $\triangle\text{ABC}\sim\triangle\text{PQR}$
$\frac{\text{AB}}{\text{PQ}}=\frac{\text{BC}}{\text{QR}}=\frac{\text{AC}}{\text{PR}}$
Therefore put the values of the known terms in the above equation to get,
$\frac{12}{9}=\frac{7}{\text{x}}=\frac{10}{\text{y}}$
On solving these simultaneous equations, we get
$\text{x}=\frac{21}{4}$
$\text{y}=\frac{30}{4}$
- We have, $\Box\text{ABCD}\sim\Box\text{PQRS}$
$\frac{\text{AB}}{\text{PQ}}=\frac{\text{BC}}{\text{QR}}=\frac{\text{CD}}{\text{RS}}=\frac{\text{DA}}{\text{SP}}$
Therefore put the values of the known terms in the above equation to get,
$\frac{20}{7}=\frac{16}{\text{x}}=\frac{50}{\text{y}}=\frac{50}{3\text{z}}$
On solving these simultaneous equations, we get
$\text{x}=\frac{28}{5}$
$\text{y}=\frac{35}{2}$
$\text{z}=\frac{35}{6}$
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