Question

Construct parallelogram ABCD in which AB=7cm,AC=10cm and BC=5cm.​

Answer 1

Answer:

ABCD is a parallelogram

AB = 7 cm

BC = 9 cm

AC = 8 cm.

In triangle ABC, AC^2 = AB^2+BC^2–2*AB*BC cos ABC,

8^2 = 7^2+9^2–2*7*9cos ABC, or

64–49–81 = -66 = –2*7*9cos ABC, or

cos ABC = 66/(2x7x9) = 0.523809523, or <ABC = arc cos 0.523809523 = 58.41186440 deg.

<BCD = 180 -<ABC = 121.5881355.

BD^2 = BC^2+CD^2–2*BC*CD cos 121.5881355

= 7^2+9^2–2*7*9*cos 121.5881355

= 49+81-2*7*9*(-0.523809523)

= 49+81+66

= 196

BD = 194^0.5 = 14 cm.

The other diagonal = 14 cm.

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