2017 · Q59
An isosceles triangle is drawn outside on one of the sides of a square as base in such a way that the perimeter of the complete figure is 7/6 times the perimeter of the original square. What is the ratio of area of the triangle to the area of the original square ?
Elementary MathematicsMensuration
- A1:1
- B2:3
- C1:2
- D1:3
Explanation
Let the square have side s; the figure's perimeter is 3s+2t = (7/6)(4s), where t is the triangle's equal side, giving t = 5s/6. The triangle's altitude is √(t²−s²/4) = 2s/3, so its area is (1/2)s(2s/3) = s²/3. The ratio to the square's area s² is 1:3. Hence option (D) 1:3.