Question

The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side , find the sides of the field.

Answer 1

(60+x)^2=(30+x)^2+(x)^2=
3600+x^2+120x=900+x^2+60x+x^2
x^2-60x-2700
(x-90)(x+30)
here x is the shortest side

Answer 2

Given:-

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.

Solution:-

Using Pythagoras theorem,

(Diagonal)² = (shorter side)² + (longer side)²

⇒(y+60)² = y² + (y+30)²

⇒y² + 3600 + 120y = y² + y²+900+60y

⇒3600+120y−y² −900−60y = 0

⇒−y² +60y+2700=0

⇒y² −60y−2700=0

⇒y² −(90−30)y−2700=0

⇒y² −90y+30y−2700=0

⇒y(y−90)+30(y−90)=0

⇒(y−90)(y+30)=0

If,

y+30=0

⇒ y=−30 (not possible)

If,

y−90=0

⇒y=90

So, the length of shorter side = y =60

Longer side 90+30=120

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