ABC is a right-angled triangle, right-angled at B such that AB = 6 cm and BC = 8 cm. What is the perimeter of the square inscribed in the triangle ABC with maximum area ?

Correct option is B

Given:

ABC is a right-angled triangle,

AB = 6 cm and BC = 8 cm

Formula Used:

Area of right-angled triangle = (Base × Height)/2

Perimeter of square = 4 × Length of a Side

Calculation:

Let the Length of a side of square inscribed = a cm

AF = 6 - a

CD = 8 - a

Area of Δ ABC = (8 × 6)/2 = 24 cm²

Area of Δ ABC = Area of Δ AFE + Area of Δ CDE + Area of square BDEF

24 = a(6 - a)/2 +a(8 - a)/2 + a²

=> a = 24/7

Perimeter of square = 4 × a = 4 × 24/7 = 96/7 cm

∴ The correct answer is 96/7 cm.