Question

What is the area of the largest rectangle that can be inscribed in right angled triangle with legs of length $3$ and $4$?

• A. $2$ sq. cm
• B. $3$ sq. cm
• C. $4$ sq. cm
• D. $5$ sq. cm

Answer 1

The correct option is B $3$ sq. cm

Let $x$ the dimension of the rectangle along the leg of length $4,$ and $y$ be the dimension of the rectangle along the leg of length $3.$

By similar reiangles$,$ $3/4=y/(4-x).$

$\therefore Y=3\left(4-x\right)4$

$\therefore$ Area of rectangle $xy=\left(3/4\right)\times \left(4-x\right)=\left(3/4\right)\left(4-{\left(x-2\right)}^2\right)=3-3{\left(x-2\right)}^2/4.$

We get so the maximum area of the rectangle is $3.$

Hence,

Option $\left(B\right)$ is correct answer