In a parallelogram PQRS, ST and RU are the perpendiculars to the sides PQ and PS. ST: RU = 3:5 and the perimeter of the parallelogram is 48 cm and area is 90 cm sq. Find the value of PT?
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Given : In a parallelogram PQRS, ST and RU are the perpendiculars to the sides PQ and PS . perimeter of the parallelogram is 48 cm and area is 90 cm sq. ST: RU = 3:5 .
To Find : value of PT
Solution:
Area of Parallelogram = PQ * ST = PS * RU = 90
=> ST / RU = PS/PQ
=> PS/PQ = 3/5
PS = 5x , PQ = 3x
2 (5x + 3x) = 48
=> 8x = 24
=> x = 3
=> PS = 15
PQ = 9
PQ * ST = 90
=> 9 * ST = 90
=> ST = 10
PS = 15
ST = 10
PT² = PS² - ST²
=> PT² = 15² - 10²
=> PT² = 125
=> PT = 5√5 = 11.18 cm
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