Solve the 17th question.
17. The sides (other than hypotenuse) of a right triangle are in the ratio 3:4. A rectangle is described on its hypotenuse,the hypotenuse being the longer side of the rectangle.The breadth of the rectangle is four-fifth of its length.Find the shortest side of the right triangle,if the perimeter of the rectangle is 180cm.
Dear Student,
Here is the solution of your asked query:
Given : The sides (other than hypotenuse) of a right angled triangle are in the ratio 3 : 4.
Let ratio coefficient = x
So,
Sides = 3x and 4x
We know :
Hypotenuse 2 = Adjacent 2 + Opposite 2
Hypotenuse 2 = ( 3x )2 + ( 4x )2
Hypotenuse 2 = 9x 2 + 16 x 2
Hypotenuse 2 = 25 x 2
Hypotenuse 2 = ( 5x ) 2
Hypotenuse = 5x
As given : The hypotenuse being the longer side of the rectangle. The breadth of the rectangle in four-fifth of its length.
So,
Length of rectangle = 5 x
And
Breadth = = 4x
We know perimeter of rectangle = 2 ( Length + Breadth )
Given : The perimeter of the rectangle is 180 cm , So
2 ( 5x + 4x ) = 180
2 ( 9x ) = 180
18 x = 180
x = 10
So,
Sides of triangle = 3 ( 10 ) = 30 cm , 4 ( 10 ) = 40 cm and Hypotenuse 5 ( 10 ) = 50 cm
Shortest side of right angle triangle = 30 cm
Regards
Here is the solution of your asked query:
Given : The sides (other than hypotenuse) of a right angled triangle are in the ratio 3 : 4.
Let ratio coefficient = x
So,
Sides = 3x and 4x
We know :
Hypotenuse 2 = Adjacent 2 + Opposite 2
Hypotenuse 2 = ( 3x )2 + ( 4x )2
Hypotenuse 2 = 9x 2 + 16 x 2
Hypotenuse 2 = 25 x 2
Hypotenuse 2 = ( 5x ) 2
Hypotenuse = 5x
As given : The hypotenuse being the longer side of the rectangle. The breadth of the rectangle in four-fifth of its length.
So,
Length of rectangle = 5 x
And
Breadth = = 4x
We know perimeter of rectangle = 2 ( Length + Breadth )
Given : The perimeter of the rectangle is 180 cm , So
2 ( 5x + 4x ) = 180
2 ( 9x ) = 180
18 x = 180
x = 10
So,
Sides of triangle = 3 ( 10 ) = 30 cm , 4 ( 10 ) = 40 cm and Hypotenuse 5 ( 10 ) = 50 cm
Shortest side of right angle triangle = 30 cm
Regards