2026 · Q78
ABCD is a parallelogram with ∠ABC = 150° and the sides have integer values. If the area of the parallelogram is 17.5 cm², then consider the following statements :
- IIt is possible to have a perimeter equal to 24 cm.
- IIIt is possible to have a perimeter equal to 72 cm.
Which of the statements given above is/are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Area = ab·sin 150° = ab/2 = 17.5 gives ab = 35. With integer sides the factor pairs are (1, 35) and (5, 7), giving perimeters 2(1 + 35) = 72 and 2(5 + 7) = 24. Both perimeters are attainable, so both statements are correct, option C.