Question

ABCD is a parallelogram and AC and BD are diagonals and they intersect at point O. If AO = 4 cm, OC = x, BO = 9 cm, and OD = y, find the value of x² + 10y. ABCD is a parallelogram and AC and BD are diagonals and they intersect at point O. If AO = 4 cm, OC = x, BO = 9 cm, and OD = y, find the value of x² + 10y.
1. 100
2. 121
3. 110
4. 109

Answer 1

Correct Answer - Option 4 : 109

Given:

AO = 4 cm, OC = x, BO = 9 cm, and OD = y

Formula used:

If ABCD is a parallelogram, and O is the intersection point of diagonals,

AO = OC, OB = OD

Calculation:

AO = OC

⇒ OC = x = 4 cm

OB = OD

⇒ OD = y = 9 cm

⇒ x² + 10y = 4² + 10 × 9 = 16 + 90

⇒ x² + 10y = 109

∴ Required answer is 109.