The altitude of a right triangle is 7cm less than its base . If the hypothenuse is 13cm , find the other two side .
Answers
Step-by-step explanation:
The traingle of a right angled triangle is 7cm less than it's base
let the base = x cm
It's height = ( x - 7 ) cm
and also given
It's Hypotenuse = 13 cm
By Pythagoras theorem
(opp)² + (ad)² = ( hyp)²
x² + (x-7)² = 13²
x² + (x²-2.x.7.7²) = 169
2x² - 14x + 49 = 169
2x² - 14x + 49 - 169 = 0
2x² - 14x - 120 = 0
2 ( x² - 7x - 60 ) = 0
x² - 12x + 15x - 60 = 0
x ( x - 12 ) + 5 ( x - 12 ) = 0
( x - 12 ) ( x + 12 ) = 0
x - 12 = 0
x = 12
OR
x + 12 = 0
x = -12 [ not belongs to Natural number ]
If the base ( x ) = 12cm
The altitude = x - 7
===> 12 - 7
===> 5cm .
Step-by-step explanation:
Given
"The Altitude of a right triangle is 7cm les than it's base"
Let the base = x
Altitude = ( x - 7 )
and also given that
hypothenuse = 13cm
we know that from
Pythagoras theorem
Hyp² = adj² + opp²
13² = ( x - 7 )² + x²
x² + ( x - 7 )² = 13²
[ Use identity (a-b)² = a² + b² - 2ab ]
x² + (x² + 7² - 2.x.7 ) = 169
x² + ( x² + 49 - 14x ) = 169
2x² + 49 - 14x = 169
2x² + 49 - 14x - 169 = 0
2x² - 14x - 120 = 0
2 ( x² - 7x - 60 ) = 0
[ Factorise the bracket terms ]
x² - ( 12x + 5x ) - 60 = 0
x ( x - 12 ) + 5 ( x - 12 ) = 0
x - 12 = 0
x = 12
And
x + 12 = 0
x = -12
Here x = -12 indicates that this number does not belongs to Natural numbers
So ,
the base = x = 12cm
the Altitude = ( x - 7 ) = 12 - 7 = 5cm