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ICSE Class 9 Answered

  
Please provide solution to Part (ii) of the above question
Asked by saif | 22 Mar, 2017, 12:47: AM
answered-by-expert Expert Answer
begin mathsize 16px style left parenthesis straight i right parenthesis space Given space that space ABCD space is space straight a space square space and space DEC space is space an space equilateral space triangle. So comma space AB equals BC equals AD equals DC and space DC equals EC equals DE rightwards double arrow AB equals BC equals AD equals DC equals EC equals DE In space increment ADE comma AD equals DE rightwards double arrow angle DAE equals angle DEA space.... left parenthesis straight i right parenthesis Similarly comma space EC equals BC rightwards double arrow angle CEB equals angle CBE space space.... left parenthesis ii right parenthesis Looking space at space the space figure comma space we space can space see space that space we space are space given space angle DEA equals angle CEB space space..... left parenthesis iii right parenthesis Now comma space angle EAB equals 90 degree minus angle DAE space space and space angle EBA equals 90 degree minus angle CBE rightwards double arrow angle EAB equals angle EBA space.... left parenthesis From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis right parenthesis rightwards double arrow AE equals BE Hence space proved. left parenthesis ii right parenthesis space In space increment DAE comma angle DEA plus angle DAE plus angle ADE equals 180 degree rightwards double arrow angle DEA plus angle DAE plus left parenthesis angle ADC plus angle CDE right parenthesis equals 180 degree rightwards double arrow angle DAE plus angle DAE plus left parenthesis 90 degree plus 60 degree right parenthesis equals 180 degree space space space space space space space space space space space space... left parenthesis Since space angles space of space straight a space square space are space 90 degree space and space angles space of space an space equilateral space triangle space are space 60 degree right parenthesis rightwards double arrow 2 angle DAE equals 30 degree rightwards double arrow angle DAE equals fraction numerator 30 degree over denominator 2 end fraction equals 15 degree end stylebegin mathsize 16px style left parenthesis straight i right parenthesis space Given space that space ABCD space is space straight a space square space and space DEC space is space an space equilateral space triangle. So comma space AB equals BC equals AD equals DC and space DC equals EC equals DE rightwards double arrow AB equals BC equals AD equals DC equals EC equals DE In space increment ADE comma AD equals DE rightwards double arrow angle DAE equals angle DEA space.... left parenthesis straight i right parenthesis Similarly comma space EC equals BC rightwards double arrow angle CEB equals angle CBE space space.... left parenthesis ii right parenthesis Looking space at space the space figure comma space we space can space see space that space we space are space given space angle DEA equals angle CEB space space..... left parenthesis iii right parenthesis Now comma space angle EAB equals 90 degree minus angle DAE space space and space angle EBA equals 90 degree minus angle CBE rightwards double arrow angle EAB equals angle EBA space.... left parenthesis From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis right parenthesis rightwards double arrow AE equals BE Hence space proved. left parenthesis ii right parenthesis space In space increment DAE comma angle DEA plus angle DAE plus angle ADE equals 180 degree rightwards double arrow angle DEA plus angle DAE plus left parenthesis angle ADC plus angle CDE right parenthesis equals 180 degree rightwards double arrow angle DAE plus angle DAE plus left parenthesis 90 degree plus 60 degree right parenthesis equals 180 degree space space space space space space space space space space space space... left parenthesis Since space angles space of space straight a space square space are space 90 degree space and space angles space of space an space equilateral space triangle space are space 60 degree right parenthesis rightwards double arrow 2 angle DAE equals 30 degree rightwards double arrow angle DAE equals fraction numerator 30 degree over denominator 2 end fraction equals 15 degree end style
Answered by Rebecca Fernandes | 22 Mar, 2017, 09:00: AM
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ICSE 9 - Maths
Ih altitudes of  a atriangle  are 10cm,12cm and 15cm, then find its semi perimeter.
Asked by npm_ninl | 05 Feb, 2018, 10:29: PM
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