Answer:

20

Step-by-step explanation:

u have to divide 60÷30= 20

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Verified answer

Hint:

Let the length of the shorter side be x, so form the equation considering the above condition that longer side is 30 metre more than the shorter side and the diagonal of a rectangular field is 60 metre more than the shorter side. And as we know that in the rectangle adjacent sides and diagonal will form a right angled triangle so apply Pythagoras theorem to it and hence on solving the value of x will be obtained.

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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 12 + Side 22

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

602 + 2(60)x + x2 = x2 + 302 + 2(30)x + x2

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

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

2700 + 60x - x2 = 0

Multiplying both sides by -1:

x2 - 60x - 2700 = 0

Solving further using quadratic formula:

Comparing x2 - 60x - 2700 = 0 with ax2 + bx + c = 0 we get,

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

b2 - 4ac = (-60)2 - 4(1)(-2700)

= 3600 + 10800

b2 - 4ac = 14400 > 0

∴ Roots exist.

x = [- b ± √ (b2 - 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

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