Answer:
the two dimensions of the rectangle are 3.5 cm and 6 cm.
Step-by-step explanation:
So, we know the perimeter is 19 cm. Which can also be represented as 2w + 2l = 19 (w = width, L = length)
We also know the area is 21 cm^2, or w*l = 21
so we have two equations:
2w + 2L = 19
wL = 21
Now, we can isolate one of the variables so that we can substitute it into the other equation.
we can isolate w by dividing the second equation by L.
w = 21/L
Now we can substitute that into the first equation:
2(21/L) + 2L = 19
42/L + 2L = 19
42 + 2L^2 = 19L
2L^2 - 19L + 42 = 0
(2L - 7) (L - 6)
L = 3.5, 6 ==> now we know the two dimensions of the rectangle are 3.5 cm and 6 cm.
