Question

please answer quickly.



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Answer 1

Given : ∆ABC is right angled triangle at C = 90°

→From the figure : BC = 12 cm , AD = 3 cm , DC = 2 cm

AC = AD + DC

= 3 cm + 2 cm

= 5 cm

→In ∆ACB,

AB² = AC² + BC² (By Pythagoras Theorem)

AB² = 5² + 12²

AB² = 25 + 144

AB² = 169

AB = ✓169

AB = 13 cm

→In ∆ABC & ∆ADC,

<BAC = <DAE (Common)

<ACB = <AED (each 90°)

∆ABC ~ ∆ADE (By A-A similarity criterion)

AB/AD = BC/DE = AC/AE

[Since corresponding sides of two similar triangles are proportional]

13/3 = 12/DE = 5/AE

→13/3 = 12/DE

13 DE = 12×3

DE = 12×3/13

DE = 36/13

→13/3 = 5/AE

13 AE = 5×3

AE = 5×3/13

AE = 15/13

•°• OPTION 'C' IS CORRECT