LA rectangle has two pairs of sides of the same length. If we call W to the width of the rectangle, we know that the length is 6cm more. If we call L the length of the rectangle:
[tex]L=W+6[/tex]The perimeter of a rectangle is twice the length plus twice the width:
[tex]Perimeter=2L+2W[/tex]Since we know that the perimeter is 52 cm, we can write the system of equations:
[tex]\begin{cases}L={W+6} \\ 2L+2W=52{}\end{cases}[/tex]We can substitute the first equation into the second one:
[tex]2(W+6)+2W=52[/tex]And solve:
[tex]2W+12+2W=52[/tex][tex]\begin{gathered} 4W=52-12 \\ . \\ W=\frac{40}{4}=10\text{ }cm \end{gathered}[/tex]We know that W = 10cm, we can now find L:
[tex]L=10+6=16\text{ }cm[/tex]Thus, the dimensions of the rectangle are:
Length: 16 cm
Width: 10 cm
