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 length of the sides of the field.

Answer 1

Let the shorter side of the rectangular field be 'x' meters.

Therefore the longer side will be (x + 30) meters.

And the length of the diagonal will be (x + 60) meters.

Now, according to the question,

The diagonal divides the rectangular into two right angled triangles and the diagonal is the common side of the two triangles and it is also the longest side of the triangles i.e. the hypotenuse.

So, by Pythagoras Theorem,

(Diagonal)² = (Smaller Side)² + (Longer Side)²

(x + 60)² = (x)² + (x + 30)²

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

x² + 60x - 120x + 900 - 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 because x = - 30 as length cannot be possible.

 

So the length of the shorter side is 90 meters and the length of the longer side is 90 + 30 = 120 meters.

There’s an alternate method too:

Let the shorter side of the rectangle be x m.
Then, larger side of the rectangle = (x + 30) m

⇒ 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.

Hope This Helps :)

Answer 2

3 0. / 2.
15
30×15
450