# 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.

**Solution:**

Let the shorter side be x meter. Then the length of the diagonal of the field will be x + 60 and the length of the longer side will be x + 30.

Using the Pythagoras theorem, the value of x can be found.

By applying Pythagoras theorem:

Hypotenuse² = Side 1^{2} + Side 2^{2}

(60 + x)^{2} = x^{2} + (30 + x)^{2}

60^{2} + 2(60)x + x^{2} = x^{2} + 30^{2} + 2(30)x + x^{2}

3600 + 120x + x^{2} = x^{2} + 900 + 60x + x^{2}

3600 + 120x + x^{2} - x^{2} - 900 - 60x - x^{2} = 0

2700 + 60x - x^{2} = 0

Multiplying both sides by -1:

x^{2} - 60x - 2700 = 0

Solving further using quadratic formula:

Comparing x^{2} - 60x - 2700 = 0 with ax^{2} + bx + c = 0 we get,

a = 1, b = - 60, c = - 2700

b^{2} - 4ac = (-60)^{2} - 4(1)(-2700)

= 3600 + 10800

b^{2} - 4ac = 14400 > 0

∴ Roots exist.

x = [- b ± √ (b^{2} - 4ac)] / 2a

= [-(- 60) ± √(14400)] / 2

= [(60) ± 120] / 2

x = (60 + 120) / 2 and x = (60 - 120) / 2

x = 180 / 2 and x = - 60 / 2

x = 90 and a = - 30

Length can’t be a negative value.

Hence, x = 90

Length of shorter side is x = 90 m

Length of longer side = 30 + x = 30 + 90 = 120 m

**Video Solution:**

## 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

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 6

**Summary:**

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, the sides of the field are 90 m and 120 m.

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