Given:
Length = 2 × width
Perimeter = 42 cm
To find:
Length and width of the rectangle
Solution:
Length = 2 × width
![l =2w](https://img.qammunity.org/2021/formulas/mathematics/middle-school/3qkf3e6mv2ru67mb9a4hp63vmfr7d275m8.png)
Perimeter =
![2(l + w)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/rormxho61r5ihkdd5riziulf53xwpej91h.png)
![2(l + w)=42](https://img.qammunity.org/2021/formulas/mathematics/middle-school/1rvtl8319ovwr4weqiksdijvbz6tyn2x42.png)
(
)
![2(3w)=42](https://img.qammunity.org/2021/formulas/mathematics/middle-school/nnv0pz7tqmw1o85pylpl50qe7tpkuuit5k.png)
![6w=42](https://img.qammunity.org/2021/formulas/mathematics/middle-school/y9wjvzhx7wakxcxdgzmxetqm3ahcw8iiu7.png)
Divide by 6 on both sides.
![$(6w)/(6) =(42)/(6)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/pglegtf9by5wlae9ixu2tm8272etllquiy.png)
w = 7
Substitute w = 7 in length.
![l =2*7](https://img.qammunity.org/2021/formulas/mathematics/middle-school/g6r8239w4suxdpmv6rcwrdkj3etcjs6myw.png)
l = 14
The length of the rectangle is 14 cm.
The width of the rectangle is 7 cm.