Aditya constructs a kite ABCD where AB = AD = 10 cm and CB = CD = 17 cm. The diagonal BD = 16 cm. During construction the diagonal AC passes through the midpoint M of BD at right angles. What is the length of AC?

Question

Accepted Answer

21. AC is the axis and meets BD at its midpoint M, so BM = 16/2 = 8. In right triangle ABM, AM = √AB^2 - BM^2 = √10^2 - 8^2 = √100 - 64 = √36 = 6. In right triangle CBM, CM = √CB^2 - BM^2 = √17^2 - 8^2 = √289 - 64 = √225 = 15. So AC = AM + CM = 6 + 15 = 21 cm.

Aditya constructs a kite ABCD where AB = AD = 10 cm and CB = CD = 17 cm.
The diagonal BD = 16 cm.
During construction the diagonal AC passes through the midpoint M of BD at right angles.
What is the length of AC?

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More Class 8 Constructing Quadrilaterals practice

Aditya constructs a kite ABCD where AB = AD = 10 cm and CB = CD = 17 cm.The diagonal BD = 16 cm.During construction the diagonal AC passes through the midpoint M of BD at right angles.What is the length of AC?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Constructing Quadrilaterals practice

Aditya constructs a kite ABCD where AB = AD = 10 cm and CB = CD = 17 cm.
The diagonal BD = 16 cm.
During construction the diagonal AC passes through the midpoint M of BD at right angles.
What is the length of AC?