2025 · Q89
A Question is given followed by two Statements I and II.
Question: ABC is isosceles with AB=AC=10. Area is 48. What is base BC?
Statement IBC is even integer.
Statement IIHeight > half the base.
Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question can be answered even without using any of the Statements
Explanation
b*h=96 and h^2+(b/2)^2=100 give b^4-400b^2+36864=0, so b=12 or 16. Statement I (even) does not decide; Statement II (h>b/2) selects b=12 (h=8>6; for b=16, h=6<8). Only Statement II alone works.