Question

The diagonal of a rectangular field is 4 metres more than the shorter side. If the longer

side is 2 metres more than the shorter side, find the sides of the field.​

Answer 1

Answer:

Let the shorter side =x m

diagonal of the rectangle =x+16 m

Longer side =x+14 m

∴(AB)

2

+(BC)

2

=(AC)

2

∴(x+14)

2

+x

2

=(x+16)

2

⇒x

2

+28x+196+x

2

=x

2

+32x+256

⇒x

2

+x

2

−x

2

+28x−32x+196−256=0

⇒x

2

−4x+60=0

⇒x

2

−10x+6x−60=0

⇒x(x−10)+6(x−10)=0

⇒(x−10)(x+6)=0

Hence, x=10 or −6

x=−6 is not admissible

So, x=10

Breadth of rectangle =10 m

Length of rectangle =10+14=24 m

Answer 2

Step-by-step explanation:

Let the shorter side =x m

diagonal of the rectangle =x+16 m

Longer side =x+14 m

∴(AB)

2

+(BC)

2

=(AC)

2

∴(x+14)

2

+x

2

=(x+16)

2

⇒x

2

+28x+196+x

2

=x

2

+32x+256

⇒x

2

+x

2

−x

2

+28x−32x+196−256=0

⇒x

2

−4x+60=0

⇒x

2

−10x+6x−60=0

⇒x(x−10)+6(x−10)=0

⇒(x−10)(x+6)=0

Hence, x=10 or −6

x=−6 is not admissible

So, x=10

Breadth of rectangle =10 m

Length of rectangle =10+14=24 m

solution