Maths-
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Question

In straight triangle A B C text , if  end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text  then  end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals

  1. s to the power of 4
  2. b squared c squared
  3. c squared a squared
  4. a squared b squared

Hint:

In this question, we have if straight triangle A B C text , if  end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text  then  end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis. We will find the area of triangle using two methods, height and base and other method using sides. Further equating both the area we will find the required value.

The correct answer is: a squared b squared


    In space straight triangle A B C comma space c squared equals a squared plus b squared comma space 2 s equals a plus b plus c
A s space i t space i s space t h e space p y t h a g o r a s space t h e o r e m comma space
A r e a space o f space t r i a n g l e space equals space 1 half cross times a b space space space _ _ _ _ _ _ _ _ _ _ _ left parenthesis i right parenthesis
A l s o comma space a s space s i d e s space a r e space a comma space b space a n d space c
S o comma space a r e a space o f space t r i n a g l e space equals 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
rightwards double arrow increment squared space equals s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis space space space _ _ _ _ _ _ _ _ _ _ left parenthesis i i right parenthesis
M u l t i p l y i n g space 4 space o n space b o t h space t h e space s i d e s comma
rightwards double arrow 4 increment squared space equals 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
F r o m space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t colon
rightwards double arrow 4 increment squared space equals 4 open parentheses fraction numerator a b over denominator 2 end fraction close parentheses squared equals space a squared b squared
S o comma space 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals a squared b squared

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