The question is from the topic quadrilaterals. In this problem perimeter and area of a rhombus are given and we have to find out the sum of the lengths of its diagonals. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. It uses the idea of area of rhombus is equal to the sum of the triangles contained in it.

Question 17: Rhombus has a perimeter of 12 and one angle = 120Â°. Find its area.

- 9 * (âˆš3)/2
- 3 * (âˆš3)/2
- 9 * âˆš3
- 18 * âˆš3

9 * (âˆš3)/2

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Perimeter = 12.

Let the side of the rhombus be â€œaâ€?, then 4a = 12 => a = 3.

One angle = 120Â°.

Adjacent angles of a rhombus are supplementary. Therefore, the other angle = 60^{Â°}.

Diagonals of a rhombus bisect each other, therefore, âˆ DAC = 60^{Â°} âˆ DCA =60^{Â°} âˆ BAC =60^{Â°}

Therefore, Triangle DAC and BAC are equilateral triangles.

Therefore, Area of Rhombus = 2 * Area of the Equilateral Triangle

= 2 * (âˆš3/4) * a^{2} = (âˆš3/2) * 9 = 9 * (âˆš3/2).

The question is **" Find the area of the rhombus"**

Choice A is the correct answer.

Â

Copyrights Â© All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{Â®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com