In the given figure, given that and quad ABCD ∼ quad PQRS. Determine the value of x, y, z in each case. 1. 2. 3.

1. We have, So the ratio of the sides of the triangles will be proportional to each other. AB PQ = BC QR = AC PR Therefore put the values of the known terms in the above equation to get, 12 9 =7 x =10 y On solving these simultaneous equations, we get x=21 4 y=30 4 2. We have, So the ratio of the sides of the quadrilaterals will be proportional to each other. AB PQ = BC QR = CD RS = DA SP Therefore put the values of the known terms in the above equation to get, 20 7 =16 x =50 y =50 3z On solving these simultaneous equations, we get x=28 5 y=35 2 z=35 6

In the given figure, given that and quad ABCD ∼ quad PQRS. Determ…

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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.

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Answer

We have, $\triangle\text{ABC}\sim\triangle\text{PQR}$

So the ratio of the sides of the triangles will be proportional to each other.

$\frac{\text{AB}}{\text{PQ}}=\frac{\text{BC}}{\text{QR}}=\frac{\text{AC}}{\text{PR}}$

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, $\Box\text{ABCD}\sim\Box\text{PQRS}$

So the ratio of the sides of the quadrilaterals will be proportional to each other.

$\frac{\text{AB}}{\text{PQ}}=\frac{\text{BC}}{\text{QR}}=\frac{\text{CD}}{\text{RS}}=\frac{\text{DA}}{\text{SP}}$

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

$\text{x}=\frac{28}{5}$

$\text{y}=\frac{35}{2}$

$\text{z}=\frac{35}{6}$