Question

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

Answer:

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Answer 2

Step-by-step explanation:

Given:-

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.

To find:-

Find the sides of the field?

Solution:-

Let the shorter side of the rectangular filed be

X m

Longer side of the rectangular field

= Shorter side + 30 m

= (X+30) m

Diagonal of the rectangular field

= Shorter side + 60 m

= (X+60) m

We know that

The diagonal of a rectangle (d) =√(l^2+b^2) units

=> (X+60) = √[(X^2+ (X+30)^2]

On squaring both sides then

=>(X+60)^2 = [√[(X^2+ (X+30)^2]]^2

=> (X+60)^2 = X^2+ (X+30)^2

=>X^2+120X+3600 = X^2+X^2+60X+900

(Since (a+b)^2 = a^2+2ab+b^2)

=> X^2+120X+3600 = 2X^2+60X+900

=> 2X^2+60X+900-X^2-120X-3600=0

=> X^2-60X-2700 = 0

=> X^2-90X+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 -30

X can not be negative

X = 90 m

Shorter side = 90 m

Longer side = 90+30 = 120 m

Diagonal side = 90+60 = 150 m

Answer:-

The sides of the given field are 120 m , 90 m

and the diagonal is 150 m

Used formulae:-

The diagonal of a rectangle (d) =√(l^2+b^2) units