Question

A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 42 insquared and a perimeter of 26 in. Find the dimensions of the brochure.
The longer side is __ in.
The shorter side is __ in.

(Type exact answers, using radicals as needed. Simplify your answers.)

Answer 1

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

$l\times b=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$2(l+b)=26\\\\\Rightarrow l+b=13\\\\\Rightarrow l=13-b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of l from equation (ii) in equation (i), we get

$(13-b)b=42\\\\\Rightarrow b^2-13b+42=0\\\\\Rightarrow b^2-6b-7b+42=0\\\\\Rightarrow (b-6)(b-7)=0\\\\\Rightarrow b-6=0,~~~b-7=0\\\\\Rightarrow b=6,7.$

Since b is the length of the shorter side, so b = 6 in.

From equation (ii), we get

$l=13-6=7.$

Thus, the length of the loner side is 7 in. and the length of the shorter side is 6 in.