Question

the hypotenuse of rectangular field is 60 m more than its smaller side and bigger is 30m more than its smaller side than measure its side

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Answer 1

Answer :

30m.

Explanation :

In a rectangular field

The hypotenuse is 60m more than and the bigger side is 30 more than it's smaller side.

Find the smaller side.

Let's assume the length of the smaller side be ‘x’

Then,

• Hypotenuse = (60 + x)
• Bigger side = (30 + x)

According to pythagoras theorem,

→ (Hypotenuse)² = (Bigger side)² + (smaller side)²

Substituting the values :

→ (60 + x)² = (30 + x)² + (x)²

Solving for ‘x’ :

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

→ 3600 + 120x + x² = 900 + 60x + 2x²

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

→ 2700 - 30x - x² = 0

→ x² + 30x - 2700 = 0

→ x² - 90x - 30x - 2700 = 0 [ splitting middle term]

→ x(x - 90) + 30(x - 90) = 0

→ (x + 30)(x - 90) = 0

→ x = 30 or, x = -90

Since, negative integer can't be a length.

∴ The value of ‘x’ is 30

Hence, the smaller side is 30m.

Answer 2

90 is the solution please chech it out