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Question:A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?
(A) 80
(B) 120
(C) 150
(D) 160
(E) 240
Approach Solution 1
A regular hexagon has six equal equilateral triangles that are of the same size, with each side measuring 80 centimeters.
Because each of the three diagonals that run through the center of the regular hexagon divides the internal 120 degrees into two 60 degree angles, we are able to deduce that the triangles are equilateral.
Consequently, w = (2) * 80, which is 160 centimeters.
D is the correct answer.
Approach Solution 2
Let's draw an ABCDEF square like the one in the picture. We need to figure out how long the BE is.
Given: It is a regular hexagon, so AB = BC = CD = DE = EF = AF = 80 cm, and each angle is 120.
Join BF and CE to make BCEF a rectangle. Angle BCE = 90
Angle CBE is 60 because the diagonal BE cuts angles ABC and DEF in half. So, triangle BCE is a 30-60-90 triangle, and the ratio of its sides is 1:3:2 (1:3:2).
So, BE = 160. The answer is D.
Approach Solution 3
Triangle in the hexagon is equilateral. You know it's equilateral because one of its angles is 60 degrees. You know it's 60 degrees because the total number of degrees in a hexagon is 720; 720/6 = 120 degrees per angle in hexagon. The triangle's sides cut that 120-degree hexagon angle in half, making 60 degrees.
The triangle has three sides that are all the same length. because of this, BC = AB = 80. The question says "diagonal," which means that the line goes all the way through the hexagon. This means that you need to double BC.
BC = 80, 80 * 2 = 160 cm.
The appropriate answer is D.
“The product of two negative integers, a and b, is a prime number p" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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