{"id":7628,"date":"2020-09-24T09:50:50","date_gmt":"2020-09-24T04:20:50","guid":{"rendered":"https:\/\/online.2iim.com\/cat-exam\/blogs\/?p=7628"},"modified":"2020-09-24T09:50:51","modified_gmt":"2020-09-24T04:20:51","slug":"cat-quants-interesting-geometry-questions","status":"publish","type":"post","link":"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-quantitative-aptitude\/cat-quants-interesting-geometry-questions\/","title":{"rendered":"CAT Quants | Interesting Geometry Questions"},"content":{"rendered":"\n
\"CAT<\/figure>\n\n\n\n

It’s the time of the year to take lots of mocks (around 10 at least)! Carefully analyse and review your mock after taking it, and then proceed to plug in the knowledge gaps! In that interest, here are a few interesting geometry questions<\/em><\/strong> for you to take a go at! The detailed solutions<\/strong><\/em> for these questions have been provided as well. Happy Solving!<\/p>\n\n\n\n

Interesting Geometry Questions<\/span>: <\/h2>\n\n\n\n

Here are a few interesting questions on basic concepts from geometry:<\/p>\n\n\n\n

1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?<\/em><\/h4>\n\n\n\n

2. Triangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?<\/em><\/h4>\n\n\n\n

3. Triangle has sides a^2, b^2 and c^2. Then the triangle with sides a, b, c has to be \u2013 <\/em><\/h4>\n\n\n\n

a) Right angled <\/em><\/p>\n\n\n\n

b) Acute-angled <\/em><\/p>\n\n\n\n

c) Obtuse angled <\/em><\/p>\n\n\n\n

d) can be any of these three<\/em><\/p>\n\n\n\n\n\n

Interesting Geometry Questions – Solutions<\/span> <\/h2>\n\n\n\n

1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?<\/em><\/h4>\n\n\n\n

This is just a counting question, with the caveat that sum of two sides should be greater than the third. Let us assume a < b < c<\/p>\n\n\n\n

a = 1, Possible triangle 1, 7, 7<\/p>\n\n\n\n

a = 2, possible triangle 2, 6, 7<\/p>\n\n\n\n

a = 3, possible triangles 3, 6, 6 and 3, 5, 7<\/p>\n\n\n\n

a = 4, possible triangles 4, 4, 7 and 4, 5, 6<\/p>\n\n\n\n

a = 5, possible triangle is 5,5,5,<\/p>\n\n\n\n

There are totally 7 triangles<\/span> possible!<\/h3>\n\n\n\n
\"math<\/figure><\/div>\n\n\n\n

2. Triangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?<\/em><\/h4>\n\n\n\n

xz = 12<\/p>\n\n\n\n

x,z can be 1, 12 or 2, 6 or 3, 4<\/p>\n\n\n\n

Possible triangles<\/em>:<\/p>\n\n\n\n