. The length of AB in the given figure: a) 8cm b) 6cm c) 4cm d) 10cm
Answers
Given : Figure
BC = 3 cm
DE = 6 cm
BD = 4 cm
AB = x cm/
To Find : Length of AB
Solution:
in Δ ABC and Δ ADE
∠A = ∠A common
∠B = ∠D = 90°
=> Δ ABC ~ Δ ADE using AA similarity
corresponding sides of similar triangles are in proportion
Hence
AB/AD = BC/ DE
AD = AB + BD
=> x/(x + 4) = 3/6
=> x/(x + 4) = 1/2
=> 2x = x + 4
=> x = 4
Length of AB is 4 cm
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![](https://hi-static.z-dn.net/files/da2/873aa2d04bb732b44626d9e8666d1fbf.jpg)
Step-by-step explanation:
BC=3 cm
DE=6 cm
BD=4 cm
AB=x cm
IN ∆ABC & ∆ ADE
Angle A = Angle A (common)
Angle B = Angle D (90°)
THEN, ∆ ABC ~∆ADE. ( BY AA SIMILARITY)
SO,.
AB/AD=BC/DE
x/x+4=3/6
6x=3x+12
3x=12
x=4 cm
Hence,length of AB is 4cm
![](https://hi-static.z-dn.net/files/d74/d177af3da6161466633f49f11b14e49e.jpg)