In the given figure, ABCD is a quadrilateral in which BC = 3 cm, AD = 13 cm, DC = 12 cm and ∠ABD = ∠BCD = 90°. Calculate the length of AB.
Pythagoras Theorem
1 Like

Question

In the given figure, ABCD is a quadrilateral in which BC = 3 cm, AD = 13 cm, DC = 12 cm and ∠ABD = ∠BCD = 90°. Calculate the length of AB.

KnowledgeBoat · Accepted Answer

In right angled triangle BCD, By Pythagoras theorem, Hypotenuse2 = Perpendicular2 + Base2 In triangle BCD, ⇒ BD2 = CD2 + BC2 ⇒ BD2 = 122 + 32 ⇒ BD2 = 144 + 9 ⇒ BD2 = 153 ⇒ BD = cm. In triangle ABD, ⇒ AD2 = AB2 + BD2 ⇒ 132 = AB2 + ()2 ⇒ 169 = AB2 + 153 ⇒ AB2 = 169 - 153 ⇒ AB2 = 16 ⇒ AB = ⇒ AB = 4 cm. Hence, length of AB = 4 cm.

Mathematics

In the given figure, ABCD is a quadrilateral in which BC = 3 cm, AD = 13 cm, DC = 12 cm and ∠ABD = ∠BCD = 90°. Calculate the length of AB.

Pythagoras Theorem

Related Questions

A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.

A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.

In the given figure, ∠PSR = 90°, PQ = 10 cm, QS = 6 cm and RQ = 9 cm, calculate the length of PR.

In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.