Answer:
The length is 22 cm and the width is 6 cm
Step-by-step explanation:
Let:
- l = length of the length of the rectangle (cm)
- w = length of the width of the rectangle (cm)
Equations:
[tex]\left \{ {{2(l + w) = 56} \atop {l = 3w + 4}} \right. [/tex]
Solve Using Substitution:
We know that l is 3w + 4. So input 3w + 4 for l in the top equation.
- 2( l + w ) = 56
- 2( 3w + 4 + w ) = 56
- 2( 4w + 4) = 56
- 8w + 8 = 56
- 8w = 48
- w = 6
Plugin New Info:
Now that we solved for w, we can solve for l by inputting the value of w in the second equation
- l = 3(6) + 4
- l = 18 + 4
- l = 22
[tex]\boxed{\text {The length is 22 cm and the width is 6 cm}}[/tex]
-Chetan K
