Question

If the length of every side of a triangle is increased by 50% then the area of the triangle will be increased by

• A. 50%
• B. 100%
• C. 125%
• D. 150%

Answer 1

The correct option is C 125%

The length of each side of triangle is a cm

Then the area of equaled triangle =$\frac{\sqrt{3}}{4}{a}^2$

iF THE SIDE OF TRIANGLE INCREASED 50% the new side=$a+\frac{50}{100}a=\frac{3a}{2}$

Then area of new triangle =$\frac{\sqrt{3}}{4}{\left(\frac{3}{2}a\right)}^2=\frac{\sqrt{3}.9a^2}{8}$

Increased in area =$\frac{\sqrt{3}.9a^2}{6}-\frac{\sqrt{3}}{4}\pi a^2=\frac{\sqrt{3}\times 5a^2}{8}$

% of Increased in area=$\frac{\sqrt{3}\times 5a^2\times 100\times 2}{\sqrt{3}\times a^2\times 8}=125$ %