A vegetable garden in rectangular shape has a total area of 84 square feet. The gardener wants to make the length 8 feet longer than the width. Find the dimensions of this garden, its width and its length?
Add an Answer
More Questions From This User See All
Answers & Comments
Answer:
The dimension of this garden are L=14; w= 6
Step-by-step explanation:
Given:
suppose the are of a rectangle is A=LW:
A= 84 square feet
L= 8+W ; w=?
Solution:
84=w\left(8+w\right)84=w(8+w)
Subtract 84 both sides:
8w+w^2-84=84-848w+w
2
−84=84−84
Simplify:
w^2+8w-84=0w
2
+8w−84=0
For quadratic equation use \quad x_=\frac{-b\pm \sqrt{b^2-4ac}}{2a}x
=
2a
−b±
b
2
−4ac
from the standard form of ax^2+bx+c=0ax
2
+bx+c=0 :
a= 1; b=8; c= -84
Substitute values to find the possible value for width:
w=\frac{-8+\sqrt{8^2-4\cdot \:1\left(-84\right)}}{2\cdot \:1}=\quad 6w=
2⋅1
−8+
8
2
−4⋅1(−84)
=6
w=\frac{-8-\sqrt{8^2-4\cdot \:1\left(-84\right)}}{2\cdot \:1}=\quad -14w=
2⋅1
−8−
8
2
−4⋅1(−84)
=−14
Substitute w=6; w= -14 to A=LW ; 84=w\left(8+w\right)84=w(8+w)
substitute 6 to w of the equation 84=w\left(8+w\right)84=w(8+w)
84=6\left(8+6\right)84=6(8+6)
84=6\left(8+14\right)84=6(8+14)
84 = 84 (correct values)
Therefore; width is equal to 6
L= 8+6 =14 ; w=6
L=14; w= 6
Answer:
the dimension of this garden are L=14; w= 6
Step-by-step explanation:
Given:
suppose the are of a rectangle is A=LW:
A= 84 square feet
L= 8+W ; w=?
Solution:
Subtract 84 both sides:
Simplify:
For quadratic equation use from the standard form of :
a= 1; b=8; c= -84
Substitute values to find the possible value for width:
Substitute w=6; w= -14 to A=LW ;
substitute 6 to w of the equation
84 = 84 (correct values)
Therefore; width is equal to 6
L= 8+6 =14 ; w=6
L=14; w= 6
PA BRAINLIEST AT PA FOLLOW THANKYOU