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

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Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Find the area of a rhombus one side of which measures 20 [#permalink]

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23 Mar 2005, 15:31
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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
Senior Manager
Joined: 15 Mar 2005
Posts: 418
Location: Phoenix
Re: PS Area of a rhombus [#permalink]

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23 Mar 2005, 16:33
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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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Manager
Joined: 15 Feb 2005
Posts: 246
Location: Rockville

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23 Mar 2005, 16:40
1
KUDOS
ar of rhombus ==> 1/2(diag1*diag2)
point of intersection makes right angles
diag 1= 24
diag 2=32
ar == 1/2(32*24)
Manager
Joined: 25 Oct 2004
Posts: 247

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23 Mar 2005, 18:48
1
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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
VP
Joined: 30 Sep 2004
Posts: 1480
Location: Germany

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24 Mar 2005, 04:23
1
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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
24 Mar 2005, 04:23
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