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Find the area of a rhombus one side of which measures 20

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Manager
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Find the area of a rhombus one side of which measures 20 [#permalink]

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New post 23 Mar 2005, 14:31
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Find the area of a rhombus one side of which measures 20 units and one diagonal 24 units

(a) 260 sq units
(b) 280 sq units
(c) 342 sq units
(d) 384 sq units
(e) 424 sq units

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Re: PS Area of a rhombus [#permalink]

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New post 23 Mar 2005, 15:33
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(D) 384.

Consider 1 triangle formed when both diagonals are drawn.

side ^ 2 = (1/2 diagonal 1)^2 + (1/2 diagonal 2)^2
400 = 144 + (1/2 diag 2) ^2
=> diag 2 = 32.

diag 1 = 24.

Area = 24 x 16 = 384.
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 [#permalink]

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New post 23 Mar 2005, 15:40
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ar of rhombus ==> 1/2(diag1*diag2)
point of intersection makes right angles
diag 1= 24
diag 2=32
ar == 1/2(32*24)

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 [#permalink]

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New post 23 Mar 2005, 17:48
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D................

(Side)^2= ((diagonal 1)/2)^2+((diagonal 2)/2)^2
(20^2= (24/2)^2 + ((diag 2)/2)^2

solving diagonal 2 =32
Area =1/2*32*24

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 [#permalink]

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New post 24 Mar 2005, 03:23
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the rhombus satisfies p^2+q^2=4a^2 where p is diag1, q is diag2 and a is on side => insert the numbers => solve for q or p => p or q is 32 => area of a rhombus = 1/2 * p * q => 1/2 * 32 * 24 = 384

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  [#permalink] 24 Mar 2005, 03:23
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Find the area of a rhombus one side of which measures 20

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