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CBSE Class 9 Answered

The side of a triangle x, x+1, 2x-1, and its area is root 10. What is the value of x.   PLEASE NOTE THAT IN YOUR ANSWER YOU TOOK AREA AS X ROOT 10. IT IS ROOT 10 ONLY MENTIONED IN THE QUESTION.
Asked by Nimmi | 14 Feb, 2019, 11:51: AM
answered-by-expert Expert Answer
we need to use Heron's formula begin mathsize 12px style square root of s open parentheses s minus a close parentheses open parentheses s minus b close parentheses open parentheses s minus c close parentheses end root space end style,
where s is semi-perimeter given by s = (a+b+c)*0.5   and a,b and c are three sides.

let a = x, b = (x+1) and c= (2x-1).
 
s  = (1/2)(x+x-1+2x-1) = 2x
 
hence
begin mathsize 12px style square root of 2 x open parentheses x close parentheses open parentheses x minus 1 close parentheses open parentheses 1 close parentheses end root space equals space square root of 10 space x squared left parenthesis x minus 1 right parenthesis space equals space 5 f left parenthesis x right parenthesis space equals space x cubed minus x squared minus 5 space equals space 0 space................... left parenthesis 1 right parenthesis end style 
 
we try different x-values to get f(x) = 0
 
f(2) = -1  ,   f(3) = 13     hence x is between 2 and 3

f(2.1) =-0.149 ,  f(2.2) = 0.808,    hence x is between 2.1 and 2.2

f(2.11) = -0.058,  f(2.12) = 0.034,   hence we take approximately x = 2.12
Answered by Thiyagarajan K | 14 Feb, 2019, 02:50: PM

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