How do we use simultaneous equations for these two questions ?
2 Answers
a)
b)
Explanation:
The length of the region to plant the Rambutan trees is given by
#P = 2l + 2w = 2(x -5) + 2(15 - y) = 2x - 10 + 30 - 2y = 2x -2y+ 20#
Since we know the perimeter is
#24 = 2x - 2y + 20#
Simplify to get:
#4 = 2x - 2y#
#2 = x - y#
#y = x -2#
Now we design the other equation. The area of the entire garden is given by
#115 = A_"total" - A_"Rambutan"#
#115= 15x- ((x-5)(15 - y))#
#115 = 15x - (15x - 75 + 5y - xy)#
#115 = 75 - 5y + xy#
We can substitute the first equation into the second now.
#115 = 75- 5(x - 2) + x(x - 2)#
#115 = 75 - 5x + 10 + x^2 - 2x#
#115 = x^2 - 7x + 85#
#0= x^2- 7x - 30#
#0 = (x - 10)(x+ 3)#
#x = 10 or -3#
Since a negative answer is impossible in this scenario, we know that
The area in metres of the region with the Rambutan trees is
Hopefully this helps!
See below.
Explanation:
Calling
and now solving for
and