Question
Download Solution PDFFind the area of a square of the maximum size which can be inscribed in a right angle triangle of side 6 cm, 8 cm, 10 cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The side of the triangle is 6 cm, 8 cm, 10 cm.
Formula used:
Area of triangle = 1/2 × base × height
Area of square = side2
Calculation:
Let the side of the square be ‘a’
Area of Δ ABC = Area of Δ ADE + Area of Δ EFC + Area of square
⇒ 1/2 × 6 × 8 = 1/2 × a × (8 – a) + 1/2 × (6 – a) × a + a2
⇒ 24 = 7a – a2 + a2
⇒ a = 24/7
Area of square = side2 = a2
⇒ (24/7)2
⇒ 576/49
∴ area of square is 576/49 cm2Last updated on Jul 18, 2025
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