Question

3. The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side
is 30 m more than its shorter side, find the sides of the field.
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Answer 1

Answer:

30 and 60 are the sides of rectangular field

Answer 2

Answer:

The sides of the rectangular field are 90m;120m;150m

Step-by-step explanation:

Given:-

The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side

diagonal of a rectangular field is 60 m more than the shorter side. If the longer sideis 30 m more than its shorter side.

To find:-

find the sides of the field.

Solution:-

Let the shorter side of the rectangle be X mThe diagonal of the rectangle=

60 m more than the shorter side=(X+60)m

The longer side=30 m more than shorter side=(X+30)m

The diagonal divides the rectangle into two right angled triangles.

so By Pythagoras theorem

(X+60)²=X²+(X+30)²

=>X²+120X+3600=X²+X²+60X+900

=>X²+120X+3600=2X²+60X+900

=>2X²+60X+900-X²-120X-3600=0

=>X²-60X-2700=0

=>X²+30X-90X-2700=0

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

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

now X+30 =0 or X-90=0

we have X=-30 or X=90

The value of X can not be negative because it is the length of the side .

Therefore,X=90m

now X+30=90+30=120m

X+60=90+60=150m

Answer:-

The shorter side=90m

The Longer side=120m

The diagonal=150 m

Used concept:-

Pythagoras Theorem:-

In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.