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.

AcademicMathematicsNCERTClass 10

Given:

The diagonal of a rectangular field is 60 meters more than the shorter side.

The longer side is 30 meters more than the shorter side.

To do:

We have to find the sides of the field.

Solution:

Let the length of the shorter side be $x$ m.

This implies, the length of the longer side$=x+30$ m.

The length of the diagonal$=x+60$ m.

We know that,

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. (Pythagoras theorem)

Therefore,

$(x)^2+(x+30)^2=(x+60)^2$

$x^2+x^2+60x+900=x^2+120x+3600$

$2x^2-x^2+60x-120x+900-3600=0$

$x^2-60x-2700=0$

Solving for $x$ by factorization method, we get,

$x^2-90x+30x-2700=0$

$x(x-90)+30(x-90)=0$

$(x-90)(x+30)=0$

$x+30=0$ or $x-90=0$

$x=-30$ or $x=90$

Length cannot be negative. Therefore, the value of $x$ is $90$.

$x+30=90+30=120$

The lengths of the sides of the field are $90$ m and $120$ m.

raja
Updated on 10-Oct-2022 13:20:12

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