3. A rectangular garden has an area of 40m² and a perimeter of 26m. The length of the garden is a cm and its width is b cm.
(a) Form two equations involving a and b.
(b) Solve these equations simultaneously in order to find the length and width
of the garden

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

what is the graph

step-by-step explanation:

21

step-by-step explanation: