Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the

Question

Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the legs.

Answer 1

If the vertical leg of the triangle is 4cm, and the base leg is 3cm, then the largest square will be formed by bisecting the 4cm and 3cm legs.

 

The resultant square will have two sides 2cm in length, and two sides 1.5cm in length.

 

We know that Area = Length x Width, so the Area will be 2cm x 1.5cm = 3cm^2.

 

If you make a drawing, you will see that all other choices will result in a lesser Area.