Question

015:} The lengths of the sides forming a right angled A is 5x cm and (3x – 4) cm.
Area of the triangle is 60 cm'. Find the hypotenuse ​

Answer 1

5xcm (3x-4 ) ×60

now I have given you the equation you can solve by your self

Answer 2

Step-by-step explanation:

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

let us take the length of the triangle AB =5x cm

and the breadth of the triangle BC =(3x-1)cm

the area of triangle =60 cm

The formula for area of the triangle=1/2(Base×Height).

then are of the triangle =∆ABC

=> 1/2(AB×BC) =60

=>1/2(5x × (3x-1))=60

=>5x(3x-1)= 60×2

=>15x²-5x =120

=>15x²-5x-120 =0

=>5(3x²-x-24) =0

=>3x²-x-24= 0

Factorisation:

=>3x²-9x+8x-24 =0

=>3x(x-3)+8(x-3) =0

=>(3x+8)(x-3) =0

=>3x+8 =0 or x-3 =0

=>3x =-8 or x=3

=> x=-8/3 or x=3.

we should take the x value always positive.

so we can take x=3.

so, AB(length)=5x=5(3)=15cm.

BC (breadth)= 3x-1 =>3(3)-1 =>9-1=8cm.

Now by using Pythagoras theorem:

AB²+BC²=AC²

AC² =(15)²+(8)²

=>AC² 225+64

=>AC² =289

=>AC=√289

=> AC= 17cm.

Hence, the hypotenuse=17cm.