Question

a quadrilateral ABCD in which angle DAB is a right angle. AB is 3.3cm, BC is 3.9cm, CD is 5.2cm and DA is 5.6cm. Find the length of BD and show that angle BCD is 90°​

Answer 1

Answer:

Part A) BD = 6.5 cm

Part B) see explanation

Step-by-step explanation:

See the attached figure

Part A) Find the length of BD

ΔDAB is a right triangle at A,  AB is 3.3cm ,  DA is 5.6cm

So, DB is the hypotenuse

Using Pythagorean equation:

DB = √(AD² + AB²) = √(3.3² + 5.6²) = √42.25 = 6.5 cm

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Part B) Show that angle BCD is 90°​

Given: CD is 5.2cm , BC is 3.9cm  and DB = 6.5 cm

So, CD² = 5.2² = 27.04

BC² = 3.9² = 15.21

DB² = 6.5² = 42.25

So, CD² + BC² = 27.04 + 15.21 = 42.25 = DB²

So, DB represent a hypotenuse at ΔBCD

So, the apposite angle of BD is a right angle

So, ∠BCD = 90°