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Question
ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.
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Solution
Given that ΔRST ~ ΔUAY.
In ΔRST, RS = 6 cm, m∠S = 50°, ST = 7.5 cm.
Given that the corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4.
`therefore "RS"/"UA"="ST"/"AY"="RT"/"UY"=5/4;`
∠S =∠A = 50º
`therefore"RS"/"UA"=5/4`
`therefore6/"UA"=5/4`
`therefore(6xx4)/5="UA"`
`therefore "UA"=4.8 "cm"`
Similarly,
`"ST"/"AY"=5/4;`
`therefore7.5/"AY"=5/4`
`therefore(7.5xx4)/5="AY"`
`therefore"AY"=6" cm"`
Therefore, In ΔUAY, UA = 4.8 cm, AY = 6 cm and m∠A = 50°
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