Question

. The difference in lengths of two adjacent sides of the right angle of a right-angled tri- angle is 1 cm. If the area of the triangle is 210 cm”, find the length of its hypotenuse​

Answer 1

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Answer 2

Let x cm be the one of the sides, then (x−7) cm be another side.

Area of triangle =60cm

2

(given)

We know, Area of triangle =

2

1

(Base×height)

⇒60=

2

1×x×(x−7)

⇒120=x

2

−7x

or x 2

−7x−120=0

Solving above equation, we have

(x−15)(x+8)=0

x=15 or x=−8

Since length measure cannot be negative, so neglect x=−8

One side =15cm

Another Side =x−7=15−7=8cm

Apply Pythagoras theorem:

Hypotenuse 2 = BasePerpendicular 2Hypotenuse

2 = (15 2+8 2 )

Hypotenuse = 289 =17

Therefore,

perimeter of triangle = Sum of all the sides =(15+8+17)cm=40cm

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