Answer:
width = 10 m
length = 16 m
Step-by-step explanation:
Formula
[tex]\textsf{Area of a rectangle} = wl[/tex]
[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]
(where [tex]w[/tex] is width and [tex]l[/tex] is length)
Given:
Substituting the given values into the formulae to create two equations:
[tex]\textsf{Equation 1}: \quad wl=160[/tex]
[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]
Rearranging Equation 1 to make w the subject:
[tex]\implies w=\dfrac{160}{l}[/tex]
Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:
[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]
[tex]\implies \dfrac{160}{l}+l=26[/tex]
[tex]\implies 160+l^2=26l[/tex]
[tex]\implies l^2-26l+160=0[/tex]
[tex]\implies l^2-10l-16l+160=0[/tex]
[tex]\implies l(l-10)-16(l-10)=0[/tex]
[tex]\implies (l-10)(l-16)=0[/tex]
[tex]\implies l=10, 16[/tex]
According to Equation 1:
As width < length, the dimensions of the shop are:
