Question

7. The length of the sides forming right-angle of
right angled triangle are 5x cm and (3x - 1)cm.
If the area of the triangle is 60 cm, find its
hypotenuse.
the smaller sides​

Answer 1

Step-by-step explanation:

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

hope it is right

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