3. A rectangular garden has an area of 40m² and a perimeter of 26m. The length of the
2 answers:
Answer:
Step-by-step explanation:
Perimeter = 2length + 2 width
2a + 2b = 26 m
Divide the equation by 2
a + b = 13 --------------(I)
a = 13 -b
Area = length *width
a*b = 40 sq.m
ab = 40 ----------------(II)
Plugin a = 13 -b in the equation (II)
(13 - b)*b = 40
13*b - b*b = 40
13b - b² = 40
0 = 40 + b² - 13b
b² - 13b + 40 = 0
Sum = - 13
Product = 40
Factors = (-8) , (-5) {-8 + (-5) = -13 & (-5)*(-8) = 40}
b² - 8b - 5b + (-8)*(-5) = 40
b(b - 8) - 5(b - 8)= 0
( b - 8) (b - 5) = 0
b - 8 =0 ; b -5 =0
b= 8 ; b = 5
Length = 8 cm
Width = 5cm
Answer:
a) a +b= 13, ab= 40
b) length= 8m, width= 5m
Step-by-step explanation:
Perimeter of rectangle= 2(length +width)
Area of rectangle= length ×width
a) Perimeter= 26m
2(a +b)= 26
Divide both sides by 2:
a +b= 26 ÷2
a +b= 13 ----- (1)
Area= 40m²
ab= 40 ----- (2)
b) From (1): a= 13 -b ----- (3)
Substitute (3) into (2):
(13 -b)(b)= 40
Expand:
13b -b²= 40
b² -13b +40= 0
Factorise:
(b -5)(b -8)= 0
b -5= 0 or b -8= 0
b= 5 or b= 8
Substitute into (3):
a= 13 -5 or a= 13 -8
a= 8 or a= 5
Since the length is usually the longer side of the rectangle, the length and the width of the rectangular garden is 8m and 5m respectively.
You might be interested in
Circle equation
(x-h)^2 + (y-k)^2 = r^2
where (h.k) is the center and r is the radius
(x -7)^2 + (y+10)^2 = 4
Answer:
ok the answer is 20
Step-by-step explanation:
This should help just.
Good luck mate:P
Answer:
The answer is x=57
Step-by-step explanation:
First, we would set the number to x.
Then, we turn the words into an equation.
x+75 = 3x-39
Isolate the x.
-2x = -114
So...
x = 57
Answer:
$206
Step-by-step explanation: