The difference of lengths of sides forming right angle in right angled triangle is 3 cm. If the perimeter of the triangle is 36 cm. Find the area of the triangle.
Answers
Answer:
Step-by-step explanation:
Difference of lengths of sides forming right angle in right angled triangle = 3cm
Perimeter of the triangle = 36 cm.
Let the length of the right angled triangle forming the right angle = x
Thus, the other side of right angled triangle will be= (x+3)
Using the pythagoras theorem we will get -
h² = p²+b²
where, Perpendicular = (x), Base = (x+3), and Hypotenuse (33-2x)
= (33-2x)² = (x+3)²+(x)²
= 4x² - 132x+1089 =x²+9+6x+x²
= 4x²- 2x²-132x-6x+1089-9 =0
= 2x²-138x+1080 = 0
= 2(x²-69x+540) = 0
Thus, x²-69x+540= 0
On solving the quadratic equation -
x(x-60)-9(x-60)=0
(x-60)(x-9)=0
x = 60 or 9
Thus, length of sides when x = 9 = 9, 12,15
Answer:
Step-by-step explanation:
Step-by-step explanation:
Difference of lengths of sides forming right angle in right angled triangle = 3cm
Perimeter of the triangle = 36 cm.
Let the length of the right angled triangle forming the right angle = x
Thus, the other side of right angled triangle will be= (x+3)
Using the pythagoras theorem we will get -
h² = p²+b²
where, Perpendicular = (x), Base = (x+3), and Hypotenuse (33-2x)
= (33-2x)² = (x+3)²+(x)²
= 4x² - 132x+1089 =x²+9+6x+x²
= 4x²- 2x²-132x-6x+1089-9 =0
= 2x²-138x+1080 = 0
= 2(x²-69x+540) = 0
Thus, x²-69x+540= 0
On solving the quadratic equation -
x(x-60)-9(x-60)=0
(x-60)(x-9)=0
x = 60 or 9
Thus, length of sides when x = 9 = 9, 12,15