The length of a rectangle is 8 m less than thrice its width. If area of the rectangle is 1675sq m them find the length and width of the rectangle
Answers
Step-by-step explanation:
As we have given,
the length of rectangle is 8m less than thrice it's width
l (length ) = 3b(breadth) - 8m
we know,
Area of rectangle = length x breadth
→ 1675 = breadth (3breadth - 8 )
→ 1675 = 3breadth ² - 8 breadth
→ 3b² - 8b - 1675 = 0
→ 3b² - 75b + 67b - 1675 = 0
→ 3b (b - 25) + 67 ( b - 25 ) = 0
→ (3b + 67) (b - 25 ) = 0
→ b = -67 / 3 , b = 25
length can never be negative
therefor, breadth or width = 25m
(length l) = 3(breadth) - 8
= 3 x 25 - 8
= 75 - 8
= 67
length = 67m
therefor the lengths and width of triangle are 67m and 25m
Answer:
Step-by-step explanation:
Given :-
length of a rectangle is 8 m less than thrice its width.
Area = 1675 sq m
To Find :-
Length and Width of the rectangle.
Solution :-
Let breadth of the rectangle( b ) = x m
length = ( 3x - 8 ) m
⇒ l × b = 1675
⇒ ( 3x - 8 ) x = 1675
⇒ 3x² - 8x - 1675 = 0
⇒ 3x² -75x + 67x - 1675 = 0
⇒ 3x( x - 25 ) + 67 ( x - 25 ) = 0
⇒ ( x - 25 )( 3x + 67 ) = 0
⇒ x - 25 = 0 or 3x + 67 = 0
⇒ x = 25 or 3x = -67
⇒ x = 25 or x = -67/3
Then, putting all values
b = x = 25 m
l = ( 3x - 8 )
l = 3 × 25 - 8
l = 75 - 8
l = 67 m
Hence, the length and width of the rectangle 67 m and 25 m