ST is parallel to RQ,PS=3cm and …

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ST is parallel to RQ,PS=3cm and SR =4cm. Find the ratio of the area of triangle PST to the area of triangle PRQ.

Posted by Khushi Tamrakar 5 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 5 years, 11 months ago

PS = 3 cm, SR = 4 cm and ST || RQ.
PR = PS + SR
= 3 + 4 = 7 cm
In $\triangle$ PST and $\triangle$ PRQ
$\angle$ SPT $\cong$ $\angle$ RPQ (common angle)
$\angle$ PST $\cong$ $\angle$ PRQ (Alternate angle)
$\triangle$ PST $\sim$ $\triangle$ PRQ (AA configuration)
$\frac { \text { ar } \Delta P S T } { \text { ar } \Delta P Q R } = \frac { P S ^ { 2 } } { P R ^ { 2 } }$ $= \frac { 3 ^ { 2 } } { 7 ^ { 2 } } = \frac { 9 } { 49 }$
Hence required ratio = 9 : 49.

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