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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Straight Lines

Olympiad workbook · IOQM · Straight Lines

In parallelogram A B C D the longer side is twice the shorter side....

In parallelogram ABCDA B C D the longer side is twice the shorter side. Let XYZWX Y Z W be the quadrilateral formed by the internal bisectors of the angles of ABCDA B C D. If the area of XYZWX Y Z W is 10 , find the area of ABCDA B C D.In parallelogram A B C D the longer side is twice the shorter side. Let X Y Z W be the quadrilateral formed by the

Correct answer

40

Step-by-step solution

In parallelogram A B C D the longer side is twice the shorter side. Let X Y Z W be the quadrilateral formed by the
As angle bisector and ⊥\perp are same. The Δ\Delta is isosceles so all the eight triangle will be of equal area  Then Required Area =(23×10)B2×10=40\text { Then Required Area }=\left(\frac{2}{3} \times 10\right) \frac{\mathrm{B}}{2} \times 10=40
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