2023 · Q79
Item contains a Question followed by two Statements. Answer each item using the following instructions : The lengths of two longer sides of the triangle Δ are 25 cm and 24 cm. Question : What is the length of the shortest side?
Statement IThe angles of Δ are in the ratio 1 : 2 : 3.
Statement IIThe length of the perpendicular drawn on the longest side of Δ from its opposite vertex is 6.72 cm.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AChoose this option if the Question can be answered by one of the Statements alone but not by the other.
- BChoose this option if the Question can be answered by either Statement alone.
- CChoose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DChoose this option if the Question cannot be answered even by using both Statements together.
Explanation
Statement I: the angles 1:2:3 make it right-angled with hypotenuse 25, so the shortest side is √(25² − 24²) = 7 — determined alone. Statement II: the altitude 6.72 to the longest side gives area ½·25·6.72 = 84; with sides 24 and 25 the cosine rule yields s² = 1201 ± 1152, i.e. s = 7 or s ≈ 48.5 — and since s is the shortest side, s = 7, also determined alone. Each statement independently answers the question (B). The stored key (A) is wrong and has been fixed.