4 Views

Question : The base of a triangle is equal to the perimeter of a square whose diagonal is $6 \sqrt{2}$ cm, and its height is equal to the side of a square whose area is 144 cm2. The area of the triangle (in cm2) is:

Option 1: 288

Option 2: 216

Option 3: 144

Option 4: 72


Team Careers360 8th Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

Correct Answer: 144


Solution : Let $a$ be the side of the first square.
Diagonal of first square = $6 \sqrt{2}$ cm
$⇒a\sqrt2 = 6 \sqrt{2}$ (where $a$ is the sides of the square)
$\therefore a = 6$
Perimeter $=4a= 4 × 6= 24$ cm
The base of the triangle, $b$ = 24 cm
Let $x$ be the side of the second square.
Area of second square = 144 cm 2
$⇒x^2 = 144$
$\therefore x = \sqrt{144} = 12$
Height of the triangle, $h$ = 12 cm
Area of the triangle = $\frac{1}{2}bh$
= $\frac{1}{2} × 24 × 12$
= $144$ cm 2
Hence, the correct answer is 144.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books