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# Rhombus ABCD has perimeter of 148, and one of its diagonals has length of 24 . What is the area of ABCD

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Rhombus ABCD has perimeter of 148, and one of its diagonals has length of 24 . What is the area of  ABCD

Dec 2, 2018

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A rhombus has 4 equal sides.....   148/4 = 37 side length

The diaonals of a rhombus bisect each other (at right angles)....we can find the 1/2 length of the other diagonal

since 1/2 of the diagonal given and the other 1/2 form a right triangle with one side of the rhombus (37) as a hypotenuse

24/2 = 12     12^2 + x^2 = 37^2      x = 35     so the other diagonal is 2*35= 70

Area Rhombus  = diagonal1 x diagonal2  /  2 =   24 x 70/2 = 840 sq units

Dec 2, 2018
edited by ElectricPavlov  Dec 2, 2018

#1
0

A rhombus has 4 equal sides.....   148/4 = 37 side length

The diaonals of a rhombus bisect each other (at right angles)....we can find the 1/2 length of the other diagonal

since 1/2 of the diagonal given and the other 1/2 form a right triangle with one side of the rhombus (37) as a hypotenuse

24/2 = 12     12^2 + x^2 = 37^2      x = 35     so the other diagonal is 2*35= 70

Area Rhombus  = diagonal1 x diagonal2  /  2 =   24 x 70/2 = 840 sq units

ElectricPavlov Dec 2, 2018
edited by ElectricPavlov  Dec 2, 2018