Question

The length of the sides forming right angle of a right-angled triangle are 5x and ( 3x−1 ) . If the area of the triangle is 60cm 2 , find its semi perimeter.

Answer 1

Answer:

Let ABC be a right angled triangle with right angle at B

let AB=5x and BC=3x−1.  

Then, area =△ABC=  

2

1

​

(Base×Height))

⇒60=  

2

1

​

(AB×BC)⇒60=  

2

1

​

×5x(3x−1)

⇒120=5x(3x−1)⇒3x  

2

−x−24=0⇒3x  

2

−9x+8x−24=0

⇒(x−3)(3x+8)=0⇒x=3or3x+8=0⇒x=3orx=−  

3

8

​

⇒x=3

AB=5x=5×3=15cm and BC=(3x−1)=(3×3−1)=8cm

Now, AC  

2

+AB  

2

+BC  

2

⇒AC  

2

=15  

2

+8  

2

⇒AC  

2

=289⇒AC=17cm

Hence, hypotenuse =17cm

Step-by-step explanation: