The sides of a right angled triangle containing the right angle are 3x+3 cm and 2x-1 cm if the area of triangle be 30cm. sq. find the length of sides of the triangle. #no spam no copy plzz.
Answers
Answer:
the sides of the triangle are 5cm 12cm 13cm
Answer:
Given
Right angle triangle
sides-
3x+3 cm
2x-1 cm
area= 30 cm²
To Find
❥Area of triangle = 1/2 x base x height
substitute the values in the above formula-
➠30 = 1/2 x (3x+3) x (2x -1)
➠30 x 2 = (3x+3) x (2x -1)
➠60 = 6x²-3x +6x -3
➠60+3 = 6x²+3x
➠63= 6x²+3x
➠2x²+x-21 =0
By solving the quadratic equation, we get-
➠(x+3) (2x- 7) = 0
➠x= 7/2 or -3
since side of triangle cannot be negative so x= 7/2
sides of triangle
➠(2x-1)= 2 x 7/2 -1
➠(2x-1)= 7-1
➠(2x-1)= 6 cm
➠(3x+3)= 3x 7/2 +3p
➠(3x+3) = 21/2 +3
➠(3x+3)= 21+6/2 = 27/2
➠(3x+3)= 13.5 cm
❥Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
By applying Pythagoras theorem we get -
hypotenuse ²= side ²+ base²
hypotenuse²= 36 + 182.25
hypotenuse = √ 218.25