Math, asked by affaquekamarali, 2 months ago

(4) PORS is a rhombus. If QR =30,
PR = 36 and the point of intersection
of diagonals PR and QS in T.
Find the area of the rhombus PQRS.​

Answers

Answered by vinitaghogale15
4

Step-by-step explanation:

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Answered by amitnrw
4

Given :  PQRS is a rhombus.  

QR =30, PR=36 and the point of intersection of diagonals PR and QS is T.

To Find  :  the area of the rhombus PQRS.​

Solution:

Diagonals of rhombus bisect each other perpendicularly

PR = 36 cm

=> RT = 36/2 = 18 cm

QR = 30 cm

ΔQTR is right angle at T

Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.

QR² = QT²  + RT²

=> 30² = QT²  + 18²

= QT²  = 30² - 18²

=> QT²  = (30  + 18)(30 - 18)

=> QT² = 48 x 12

=> QT² = 12 x 4 x 12

=> QT  = 12 x 2

=> QT = 24 cm

Hence diagonal QS = 2 * 24 = 48 cm

Area of rhombus = (1/2) * diagonal 1 * diagonal 2

= (1/2) * 36 * 48

=36 * 24

= 864

area of the rhombus PQRS.​ = 864  sq units

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