Question

the diagonal of a rectangular field is 60 meters more than the shorter side if the longer side is 30 meter than the shorter side find the side of the field​

Answer 1

Step-by-step explanation:

let the shorter side be x

then longer side=x+30

and diagonal =x+60

by Pythagoras theoram

(x+60)^2=x^2+(x+30)^2

=x^2+3600=x^2+x^2+900

=3600-900=2x^2-x^2

=2700=x^2

=x=√2700=60(approx.)

so breadth=60m

and length =90m

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Answer 2

Given:-

• The diagonal of a rectangular field is 60 meters
• The longer side is 30 meter.

To find:-

• Find the side of the field.?

Solutions:-

• Let the shorter side of the rectangle be x m.

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

Diagonal of the rectangle = √x² + (x + 30)²

The diagonal of the rectangle is 60 m more that the shorter side.

Therefore,

=> √x² + (x + 30)² = x + 60

=> 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 = 0 or x + 30 = 0

=> x = 90 or x = - 30

Side cannot be negative

Therefore, the length of the shorts side be 90m

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

Hence, the side of the field is 120m.