Math, asked by srikanthd, 3 months ago

In ∆ABC, angle A = 90°, AD is the bisector of angle A meeting BC at D, and DE is perpendicular to AC at E. If AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:​

Answers

Answered by piseprachiti5
4

Answer:

Hi mate

HERE IS YOUR ANSWER

HOPE IT HELPS

Step-by-step explanation:

Since, < CED = < CAB ( each being 90°)

=> ED // AB

=> < CDE = <CBA ( corresponing angles formed by // lines)

=> tri CED ~ tri CAB ( by AA similarity corollary)

=> CE/CA = ED/AB ( csst)

=> x/ 6 = DE/ 4

But DE = EA ( as tri EAD is isosceles, being each base angle = 45° ) & EA= 6 - x

=> x/6 = ( 6- x) / 4

=> 4x = 36 - 6x

=> 10x = 36

=> x = 3.6

=> DE = 6-x = 6 - 3.6 = 2.4 cm

=> 12/DE = 12/ 2.4 = 5

12/DE = 5 cm . . . . . . .Ans

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