the diagonal of a rectangular field is 60m more than its breadth If it's length is 30m more than the breadth,find the length and breadth of the field
Answers
Step-by-step explanation:
Let the breadth be x and y.
(y+30)^2+y2=(y+60)^2
y^2+60y+900+y^2=y^2+120y+3600.
y^2-60y=3600-900
y^2-60y-2700=0
y^2-90y+30y-2700=0
y(y-90)+30(y-90)=0
(y-90)(y+30)=0
Breadth = 90 m
Length = 120 m.
Answer:
Shorter side is 90 m and bigger side is 120 m.
Step-by-step explanation:
Given :
The diagonal of a rectangular field is 60mmore than its breadth.If its length is 30m more than its breadth.
To find :
Length and breadth of rectangular field.
Solution :
Consider -
- Length of shorter side = x
- Length of bigger side = (x + 30)
- Length of diagonal = (x + 60)
Using Pythagoras theorem,
(Hypotenuse)² = (Base)² + (Height)²
⇒ (x + 60)² = (x + 30)² + x²
⇒ x² + 120x + 3600 = x² + 60x + 900 + x²
⇒ 60x + 2700x = x²
⇒ x² - 60x - 2700 = 0
⇒ x² - 90x + 30x - 2700 = 0
⇒ x(x - 90) + 30(x - 90) = 0
⇒ x = -30 and 90
⇒ x = 90
Short side = 90 m
★ Bigger side -
⇒ 90 + 30
⇒ 120 m
Therefore, Shorter side is 90 m and bigger side is 120 m.