Question

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side. Find the sides of the field. ​

Answer 1

Answer:

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Answer 2

Answer:

We have,

Long side of rectangular field is 60 meters more then the shorter side.

Let the longer side will be (y+30)mtr.

And the length of the diagonal will be (y+60) mtr.

Now, According to given question.

Using Pythagoras theorem,

(Diagonal)

2

=(shorterside)

2

+(longerside)

2

(y+60)

2

=y

2

+(y+30)

2

⇒y

2

+3600+120y=y

2

+y

2

+900+60y

⇒3600+120y−y

2

−900−60y=0

⇒−y

2

+60y+2700=0

⇒y

2

−60y−2700=0

⇒y

2

−(90−30)y−2700=0

⇒y

2

−90y+30y−2700=0

⇒y(y−90)+30(y−90)=0

⇒(y−90)(y+30)=0

If,

y+30=0

y=−30(notpossible)

If,

y−90=0

y=90

So, the length of shorter side =y−30=90−39=60

Longer side 90+30=120

Hence, this is the answer.