A rectangle has a perimeter Of 19 cm it’s areas 21 cm² find its dimensions

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.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2