the difference between the length of a side of a right triangle which form the right angle is 3 cm if it's perimeter is 36cm find the lengths of the sides
Answers
HEY THERE!!
Method of Solution!
Suppose the actual length of right Angled Triangle which form the right angle 'x'.
Now, According to the Question Statement!
Other side of right angled triangle = (x+3)
Also, Using Pythagoras theorem!
h²=P²+b²
Here, Before using Pythagoras theorem find the lengths side(Hypotenuse) of right angled triangle!
Measure of hypotenuse Side!
36-x-(x+3)
= 36-x-x-3
= 36-2x-3
=36-3-2x
=33-2x
Now, Using Pythagoras theorem!
here, Base = (x+3), Perpendicular = (x) and Hypotenuse (33-2x)
Substitute the Given value in Equation Formula!
h²=p²+b²
(33-2x)² = (x+3)²+(x)²
1089+4x²-2.2x.33 = x²+9+2.3.x+x²
4x²-132x+1089=x²+9+6x+x²
4x²-132x+1089=2x²+6x+9
4x²-2x²-132x-6x+1089-9=0
2x²-138x+1080 = 0
2(x²-69x+540) = 0
So, x²-69x+540= 0
Solving the Quadratic Equation!
x²-69x+540 = 0
x²-60x-9x+540=0
x(x-60)-9(x-60)=0
(x-60)(x-9)=0
x=60 or 9
Now, According to the Question statement!
Length of sides = 9, 12,15
Also, Length of sides = 60,63,-87.
Thanks!
Here is your solutions
Let
length of right Angled Triangle which form the right angle x
A/q
Other side of right angled triangle = (x+3)
Now
To find the lengths side(Hypotenuse) of right angled triangle:-
hypotenuse = 36-x-(x+3)
= 36-x-x-3
= 36-2x-3
=36-3-2x
=33-2x
Hence ,
We have
Base = (x+3)
Perpendicular = (x)
Hypotenuse (33-2x)
Putting Given value in formula :-
Using Pythagoras theorem
h²=p²+b²
(33-2x)² = (x+3)²+(x)²
=>1089+4x²-2.2x.33 = x²+9+2.3.x+x²
=>4x²-132x+1089=x²+9+6x+x²
=>4x²-132x+1089=2x²+6x+9
=>4x²-2x²-132x-6x+1089-9=0
=>2x²-138x+1080 = 0
=>2(x²-69x+540) = 0
=>x²-69x+540= 0
=>x²-69x+540 = 0
=>x²-60x-9x+540=0
=>x(x-60)-9(x-60)=0
=>(x-60)(x-9)=0
=>x = 60 or 9
when x = 9
Base = (x+3) = 9 +3 =12✔
Perpendicular = (x) = 9✔
Hypotenuse (33-2x) = 33 -2×9 = 15✔
side of triangle =12 9 33
when x = 60
Base = (x+3) = 9 +3 =63✔
Perpendicular = (x) = 60✔
Hypotenuse (33-2x) = -87 ✔
side of triangle 60, 63, -87
Hope it helps you