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ICSE Class 9 Answered

If the area of an isosceles traingle is 60 cm^2 and the length of each of its equal sides is 13 cm , find its base .
Asked by aadrica.kanika | 17 Oct, 2018, 06:37: PM
answered-by-expert Expert Answer
Given:
ΔABC is an isosceles triangle.
AB = AC = 13 cm
 
Constaruction:
Draw AD perpendicular to BC with height h.
Therefore BD = CD = a   (Isosceles triangle)
begin mathsize 16px style In space increment ABD comma AB squared to the power of space space end exponent equals space AD squared plus space BD to the power of 2 space space end exponent space space space left parenthesis By space pythagoras space theorem right parenthesis rightwards double arrow 13 squared to the power of space space end exponent equals space straight h squared plus space straight x squared space space space.... left parenthesis straight i right parenthesis Area space of space increment ABC space equals space 1 half cross times space straight b space cross times space straight h rightwards double arrow 60 space equals 1 half cross times space 2 straight x space cross times space straight h rightwards double arrow 120 space equals space 2 xh space space space space space space space space space space space space space.... left parenthesis ii right parenthesis Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space 17 space equals space straight x space plus space straight h space space space space... left parenthesis iii right parenthesis straight h space equals space 17 space minus space straight x Put space the space value space of space straight h space in space left parenthesis ii right parenthesis comma space we space get straight x squared space minus space 17 space straight x space plus space 60 space equals space 0 After space solving space comma space we space get straight x space equals space 5 space or space straight x space equals space 12 If space straight x space equals space 5 space comma space BC thin space equals space 2 straight x space equals space 10 space If space straight x space equals space 12 space comma space BC space equals space 2 straight x space equals space 24 space space end style
 
 
Answered by Yasmeen Khan | 18 Oct, 2018, 11:53: AM

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