Question

The diagonal of a rectangular field is 60 metresmore than the shorter side .if the longer side is 30 metres more than tje shorter side, fine the sides of the field

Answer 1

hey mate

here is your answer

Answer 2

Here your answer goes

Step :-1

Let ABCD be the rectangular field

AC is diagonal

Let the Shorter side = AB = x m

Step :- 2

Given ,

Diagonal of a rectangular field is 60 meters more than the shorter side

x + 60 meter

Longer Side is 30 meters more than the Shorter Side

x + 30 meter

Step :- 3

We know that ,

All angles of  a rectangle are right angle

In ΔABC

∠B = 90°

Hence , ABC is a right angle triangle

Step :- 4

Apply Pythagoras theorem in ΔABC

$AC^2 = AB^2 + BC^2$

⇒ $(x+60)^2 = x^2 + (x + 30 )^2$

⇒ $x^2 + 60^2 + 2 * x * 60 = x^2 + x^2 + 30^3 + 2* x * 30$

⇒ $x^2 + 60 * 60 + 120x = x^2 + x^2 + 30 * 30 +2 * x* 30$

⇒ $x^2 + 3600 + 120 = x^2 + x^2 + 900 + 60x$

⇒ $x^2 + 3600 + 120 - x^2 - x^2 - 900 - 60 = 0$

⇒ $x^2 - x^2 - x^2 + 120 - 60x + 3600 - 900$

⇒ $-x^2 + 60x + 2700 = 0$

⇒ $x^2 - 60x - 2700 = 0$

Step :- 5

Since , We get a Quadratic Equation WE can Solve it further by factorization

⇒ $x^2 - 60x - 2700 = 0$

⇒ $x^2 - 90x + 30x - 2700 = 0$

⇒ $x (x - 90) +30 ( x - 90 )$

⇒ ( x - 90 ) ( x + 30 )

⇒ x = 90 and - 30

Since , Length ( x ) cannot be negative

x = 90

Therefore , Shorter Side of the field x = 90 meters

Longer Side of the field

=> x + 30

=>   90 + 30

=> 120 meters

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