Question

A tapzium PQRS where PQ=12m and PS=13m if PT=13m and the area and perimeter of trapzium are 150m square and 54.7m respectively,find length​

Answer 1

$\huge\underline\red{\sf CorrectQuestion :-}$

★ A tapzium PQRS where PQ=12m and PS=13m , if PT=10m and the area and perimeter of trapzium are 150m square and 54.7m respectively, then find the length of RS & QR

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Given

• Length of PQ is 12 m and PS is 13 m
• PT ( Height) is 10 m
• Area and Perimeter of trapezium is 150m² and 54.7 m respectively

To Find:

• Length of RS and QR

Solution:

★ Area of trapezium = 1/2 ( Sum of parallel sides) x Distance between them

$\small\implies{\sf }$ Area of PQRS = 1/2 ( PQ + SR ) x PT

$\small\implies{\sf }$ Area of PQRS = 1/2 ( 12 + SR ) x 10

$\small\implies{\sf }$ 150 = 1/2 ( 120 + 10SR)

$\small\implies{\sf }$ 150 x 2 = 120 + 10SR

$\small\implies{\sf }$ 300 – 120 = 10SR

$\small\implies{\sf }$ 180 = 10SR

$\small\implies{\sf }$ 180/10 = SR

$\small\implies{\sf }$ 18 m = SR

Hence, The Length of SR is 18 m.

A/q

★ Perimeter of Trapezium = Sum of all sides ★

$\small\implies{\sf }$ Perimeter = PQ + QR + RS + SP

$\small\implies{\sf }$ Perimeter = 12 + QR + 18 + 13

$\small\implies{\sf }$ 54.7 = 43 + QR

$\small\implies{\sf }$ 54.7 – 43 = QR

$\small\implies{\sf }$ 11.7 = QR

Hence, The Length of QR is 11.7 m.