Maths-
General
Easy

Question

In triangle A B C comma i f c squared equals a squared plus b squared comma 2 s equals a plus b plus c then 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

hintHint:

In this question we have to calculate the area of triangle use the heron formula and then using right angle triangle increment equals 1 half b a s e cross times h e i g h t. Then equate them to find the answer.

The correct answer is: a squared b squared


    In this question we are given c squared equals a squared plus b squared,2 s equals a plus b plus c and we have to find the value of 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
    Step1: Using the property of Right angle triangle
    It is given that c squared equals a squared plus b squared, therefore side c is the hypotenuse and Sides a comma b are base and height
    We know that area of a right angle triangle is increment equals 1 half b a s e cross times h e i g h t
    increment equals 1 half a b
    Step2: Using Heron Formula
    increment equals square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root
    By squaring both sides we get,
    increment squared equals s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
    By multiplying by 4 both sides we get,
    4 increment squared equals 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
    =>increment squared equals 1 fourth a squared b squared
    4 increment squared equals 4 cross times 1 fourth a squared b squared
    =>a squared b squared

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