Question

Mario is constructing a frame for a 10 in .by 8 in. photo. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. What is the dimension of the frame? But can someone please break it down??

Answer 1

Answer:

Width of the frame = 1 in

Explanation:

Given the dimension of the photo to be 10in by 8in, then the area of the photo will be;

$10\times8=80in^2$

Then the area of the frame can be determined as;

$120-80=40in^2$

Let the width of the frame be w, we can determine the value of w as follows;

$\begin{gathered} (10+2w)(8+2w)=120 \\ 80+20w+16w+4w^2=120 \\ 4w^2+36w+80=120 \\ w^2+9w+20=30 \\ w^2+9w-10=0 \end{gathered}$

We have to solve the resulting quadratic equation by finding two factors of -10 whose sum will give +9, the numbers are 10 and -1.

We can then split the middle term of the quadratic equation as follows;

$\begin{gathered} w^2+10w-w-10=0 \\ w(w+10)-1(w+10)=0 \\ (w+10)(w-1)=0 \\ \therefore w+10=0 \\ w=-10 \\ \\ w-1=0 \\ w=1 \end{gathered}$

So we'll go with the positive number, w = 1