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.
Answers
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
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