Question

Please give me answer with solution please... please...​

Answer 1

Answer:

90 m and 120m

Step-by-step explanation:

Let us say, the shorter side of the rectangle be x m.

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

As given, the length of the diagonal is = x + 30 m

Therefore,

⇒ 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) = 0

⇒ (x – 90)(x + 30) = 0

⇒ x = 90, -30

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

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

Answer 2

$\huge{\green{\cal{\dag{\underline{\underline{Solution}}}}}}$

AC is a diagonal

AB and BC are the sides

angle ABC = 90° [angle of rectangle]

∴ ∆ ABC is a right triangle.

⇒AC² = AB² + BC²

(x+60)² = x² + (x+30)²

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

x² + 60x + 900 - 120x - 3600 = 0

x² - 60x - 2700 = 0

x² + 30x - 90x -2700 = 0

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

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

x = -30 or x = 90

But side cannot be negative

∴ x = 90

x + 30 = 90 + 30 = 120

$\Large{\green{\cal{\underline{\underline{Conclusion}}}}}$

Length = x + 30 = 120 m

Breadth = x = 90 m