In the figure given below, ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD = 9 cm and DC = 4 cm, then what is the length of BD?
6 cm
Concept:
Pythagoras theorem:
It states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Calculation:
Given, AD = 9 cm and DC = 4 cm
⇒ AC = AD + DC = 9 + 4 = 13 cm
In ∆ABC and ∆ADB, side AB is common, ∠ABC = ∠ADB = 90°
Also, ∠BAC = ∠BAD (common angle)
⇒ ∆ABC and ∆ADB are similar triangles, hence, the ratio of their corresponding sides is equal,
⇒ AB/AD = AC/AB
⇒ AB 2= AC × AD = 13 × 9 = 117
Now, in ∆ADB,
⇒ AB 2= AD 2+ BD 2
⇒ 117 = 81 + BD 2
∴ BD = √36 = 6 cmWhat is the area of quadrilateral ABCD?
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