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CBSE Class 9 Answered

the triangle  sides are x,x+1, 2x-1 and its area is root 10. What is the value of x
Asked by Nimmi | 13 Feb, 2019, 11:09: AM
answered-by-expert Expert Answer
Question should be :
The triangle  sides are x,x+1, 2x-1 and its area is xbegin mathsize 16px style square root of 10 end style. What is the value of x
Solution:
begin mathsize 16px style straight s space equals space fraction numerator straight x space plus space straight x space plus space 1 space plus space 2 straight x space minus space 1 over denominator 2 end fraction equals space 2 straight x
By space Herons apostrophe space Formula colon
Area space of space straight a space space triangle space equals space square root of straight s left parenthesis straight s space minus space straight a right parenthesis space left parenthesis straight s space minus space straight b right parenthesis left parenthesis straight s space minus space straight c right parenthesis space end root
Here space straight a space equals space straight x comma space straight b space equals space straight x space plus space 1 space and space straight c space equals space 2 straight x space minus space 1
After space substituting space the space values comma space we space get
rightwards double arrow straight x square root of 10 equals space square root of 2 straight x cubed space minus space 2 straight x squared end root
Squaring space on space both space the space sides comma space we space get
10 straight x squared space equals space 2 straight x cubed space minus space 2 straight x squared
rightwards double arrow 2 straight x to the power of 3 space space end exponent minus space 12 straight x squared space equals space 0
rightwards double arrow straight x to the power of 3 space space end exponent minus space 6 straight x squared space equals space 0
rightwards double arrow straight x squared space open parentheses straight x space minus space 6 close parentheses space equals space 0 space
rightwards double arrow straight x squared space equals space 0 space or space space straight x space minus space 6 space equals space 0
rightwards double arrow straight x space equals space 0 space or space straight x space equals space 6
Length space can apostrophe straight t space be space zero.
straight x space equals space 6 space end style
Answered by Yasmeen Khan | 13 Feb, 2019, 01:10: PM
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