Question

The diagonal of a rectangular field is 16 metres more than the shorter side. if the longest side is 30 metres more than the shorter side find the sides of the field.

Answer 1

Question:

The diagonal of a rectangular field is 16 metres more than the shorter side. if the longest side is 30 metres more than the shorter side find the sides of the field.

Answer:

Length of the shorter side= 90m

Length of greater side will be=120 m

Step-by-step explanation:

• Let shorter side of rectangle= X meter
• Larger side= x+30 meter

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

Refer to the attachment

Howeve, side cannot be negative.

• Therefore,Length of the shorter side= 90m
• Length of greater side will be=30+90=120 m

$\huge \bold {{@QianNiu}}$

Answer 2

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 =(x+16) 2

⇒x 2 +28x+196+x 2 =x 2+32x+256

⇒x 2 +x 2−x 2+28x−32x+196−256=0

⇒x2 −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