Respuesta :
Answer: The length of the loner side is 7 in. and the length of the shorter side is 6 in.
Step-by-step explanation: Given that a graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 42 in squared and a perimeter of 26 in.
We are to find the dimensions of the brochure.
Let l and b represents the lengths of the longer side and shorter side respectively of each page of the brochure.
Then, according to the given information, we have
[tex]l\times b=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]2(l+b)=26\\\\\Rightarrow l+b=13\\\\\Rightarrow l=13-b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of l from equation (ii) in equation (i), we get
[tex](13-b)b=42\\\\\Rightarrow b^2-13b+42=0\\\\\Rightarrow b^2-6b-7b+42=0\\\\\Rightarrow (b-6)(b-7)=0\\\\\Rightarrow b-6=0,~~~b-7=0\\\\\Rightarrow b=6,7.[/tex]
Since b is the length of the shorter side, so b = 6 in.
From equation (ii), we get
[tex]l=13-6=7.[/tex]
Thus, the length of the loner side is 7 in. and the length of the shorter side is 6 in.
