In ∆ABC, right angled at A, if AD⟂ to BC, prove that AB² + CD² = BD² + AC²
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)
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a rectangular plot of land masses 41 m in length and 22.5 M invite a boundary wall 2 metre high is built all around the plot at a distance of 1.5 m from the plot find the inner surface area of the boundary wall
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[FIGURE IS IN THE ATTACHMENT]
SOLUTION:
In right angled ∆BDA ,
AB²= AD²+ BD²……………(1)
[By Pythagoras theorem]
In right angled ∆CDA ,
AC²= CD²+AD²…………….(2)
[By Pythagoras theorem]
ON SUBTRACTING EQUATION 2 FROM EQ 1 we get,
AB² - AC² = BD²-CD²
AB²+CD²= BD²+AC²
Hence proved….
HOPE THIS WILL HELP YOU….
SOLUTION:
In right angled ∆BDA ,
AB²= AD²+ BD²……………(1)
[By Pythagoras theorem]
In right angled ∆CDA ,
AC²= CD²+AD²…………….(2)
[By Pythagoras theorem]
ON SUBTRACTING EQUATION 2 FROM EQ 1 we get,
AB² - AC² = BD²-CD²
AB²+CD²= BD²+AC²
Hence proved….
HOPE THIS WILL HELP YOU….
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