The prependicular of a right angle triangle is 7cm less than its base of hypotenuses is 13cm find the remaining 2sides of the triangle
Answers
ANSWER :
Hypotenuse = 13 cm
Let the base of the triangle be 'x'
But it is given that the perpendicular is 7cm less than the base
Let the perpendicular be (x - 7).
Using the Pythagoras theorem:
13^2 = (x)^2 + (x-7)^2
=> 169 = x^2 + x^2 + 49 - 14x
=> 169 = 2x^2 + 49 - 14x
=> 169 - 49 = 2x^2 - 14x
=> 120 = 2x^2 - 14x
=> 2x^2 - 14x - 120 = 0
=> 2 ( x^2 - 7x - 60 ) = 0
=> x^2 - 7x - 60 = 0
=> x^2 - 12x + 5x - 60 = 0
=> x ( x - 12) + 5 ( x - 12 ) = 0
=> ( x + 5 ) ( x - 12 ) = 0
Now, equate the terms to zero to find the values of x
=> x + 5 = 0 or x - 12 = 0
=> x = - 5 or x = 12
As it is distance, the value cannot be negative. Therefore, reject the negative value
=> Base of the triangle = x = 12 cm
=> Perpendicular = x - 7 = 5 cm
Therefore, the other two sides measure 12 cm and 5 cm
Hope this helps you ☺☺