27. In a school of 500 students, 125 like chess and 160 like badminton. 45 students like chess and badminton both. Find how many
1 answer:
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Answer:
392
Step-by-step explanation:
Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.
Extend lines XQ, YR, YS and XP and mark their intersection as A and B.
Quadrilateral XAYB is a square because all right triangles PXQ, QAR, RYS and SBP are congruent (by ASA postulate) and therefore
- all angles of the quadrilateral XAYB are right angles
- all sides of XAYB are congruent and equal to 6 + 8 = 14 units.
Segment XY is the diagonal of the square XAYB, by Pythagorean theorem,