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 sides of the field.​

Answer 1

Let shorter side be = (x) m.

So, diagonal = (60 + x) m.

Again, longer side = (30 + x) m.

We know,

$\boxed{d = \sqrt{l^2 + b^2}}$

(d = diagonal.)

So,

(60 + x) = √[(30 + x)² + x²]

=> x + 60 = √[2x² + 60x + 900]

By squaring both sides,

(x + 60)² = 2x² + 60x + 900

=> x² + 120x + 3600 = 2x² + 60x + 900

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

=> - x² + 60x + 2700 = 0

=> x² - 60x - 2700 = 0

=> x² - (90 - 30)x - 2700 = 0

[Use the quadratic formula if you find it difficult to factor.]

=> x² - 90x + 30x - 2700 = 0

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

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

∴ Either, x = - 30 or x = + 90.

Therefore rejecting the first value, we get size of breadth as 90 m. (As side cannot be negative.)

And, l = (30 + 90) m = 120 m.

Hint:

Quadratic formula:

$\boxed{x = \dfrac{- b \pm \sqrt{b^2-4ac} }{2a}}$

More:-

Have you ever heard about extraneous roots and unreal or imaginary roots?

• Extraneous roots do not satisfy the quadratic equation. Or, putting their values in place of the varible won't fetch you 0!
• Imaginary roots do not exist really.

Answer 2

Answer:

Let the length of the shorter side be x metres.

The length of the diagonal= 60+x metres

The length of the longer side =30+x metres

Applying Pythagoras theorem,

Diagonal²=longer side²+shorter side²

(60+x) ²= (30+x) ² + x²

3600+120x+x²=900+60x+x²+x²

2700+60x-x²=0

2700+90x-30x-x²=0

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

X=90,

Shorter side is 90m, longer side is 90+30=120m

Step-by-step explanation:

l hope it will help u ☺️☺️☺️☺️