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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. - CBSE Class 10 - Mathematics

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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.

Solution 1

Let the shorter side of the rectangle be x m.

Then, larger side of the rectangle = (x + 30) m

Diagonal of rectangle = `sqrt(x^2+(x+30)^2)`

It is given that the diagonal of the rectangle = (x+30)m

`:.sqrt(x^2+(x+30)^2) = x +60`

⇒ x2 + (x + 30)2 = (x + 60)2

⇒ x2 + x2 + 900 + 60x = x2 + 3600 + 120x

⇒ x2 - 60x - 2700 = 0

⇒ x2 - 90x + 30x - 2700 = 0

⇒ x(x - 90) + 30(x -90)

⇒ (x - 90)(x + 30) = 0

⇒ x = 90, -30

However, side cannot be negative. Therefore, the length of the shorter side will be 90 m.

Hence, length of the larger side will be (90 + 30) m = 120 m.

Solution 2

Let the length of smaller side of rectangle be x meters then larger side be (x + 30) meters and their diagonal be (x + 60)meters

Then, as we know that Pythagoras theorem

x2 + (x + 30)2 = (x + 60)2

x2 + x2 + 60x + 900 = x2 + 120x + 3600

2x2 + 60x + 900 - x2 - 120x - 3600 = 0

x2 - 60x - 2700 = 0

x2 - 90x + 30x - 2700 = 0

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

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

x - 90 = 0

x = 90

Or

x + 30 = 0

x = -30

But, the side of rectangle can never be negative.

Therefore, when x = 90 then

x + 30 = 90 + 30 = 120

Hence, length of smaller side of rectangle be 90 meters and larger side be 120 meters.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 4: Quadratic Equations
Ex.4.30 | Q: 6 | Page no. 88
Solution 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. Concept: Solutions of Quadratic Equations by Completing the Square.
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