Question

find the area of a rhombus one side of which measures 20 cm and one of whose diagonals is 24 cm

Answer 1

Let PQRS be a rhombus whose side is 20cm . Let the diagonal PR and QS intersect each other at T. Let QS measure 24cm . The diagonals of a Rhombus bisect each other at right angles and angle PTQ is a right angle.In ∆PTQ using Pythagoras theorem:
= PT^2 + QT^2 = PQ^2
= PT^2 + 10^2 = 20^2
= PT^2 + 100
= 200= PT^2 = 200 - 100
= 100= PT^2 = 10 ( Sq. root of 100 )
PR = 2 x PT= 2 x 10= 20.
Area of Rhombus = 1/2 x d1 x d2.
= 1/2 x 20 x 24
= 240m^2
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