Question

the diagonal of a rectangular field is 60 M 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:

Shortest side of rectangle is 90 m ,

Longer side of rectangle is 30 +90 = 120 m

and diagonal of rectangle  is 60+90 = 150 m

Step-by-step explanation:

Consider, ABCD be the rectangle.

Let the shorter side of rectangle be x m

Then according to question

longer side will be ( x + 30 ) m and diagonal will be ( x + 60 ) m.

Since ABC forms a right angled triangle with ∠B = 90°

In ΔABC , applying Pythagoras theorem,

Pythagoras theorem states that the sum of square of base and perpendicular of a triangle is equal to the square of hypotenuse.

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

Putting values for each sides,

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

Evaluate, $(a+b)^2=a^2+b^2+2ab$

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

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

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

$x^2-60x-2700=0$

Solving the quadratic equation using splitting middle term method,

$x^2+30x-90x-2700=0$

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

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

⇒x = 90 and x = -30

Since x is side of rectangle then x cannot be negative.

So, shortest side of rectangle is 90 m

Longer side of rectangle is 30 +90 = 120 m

and diagonal of rectangle  is 60+90 = 150 m

Answer 2

Answer:

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