Question

Mario is constructing a frame for 10 in. by 8 in. photo. He wants the frame to be the same with all the way around in the same area of the frame and photo to be 120 square inches

What is the dimension of the frame?

Answer 1

Answer: 12 in. by 10 in.

Step-by-step explanation:

Given: The dimensions of photo is 10 in. by 8 in.

Therefore, Area of photo= $10\times8=80\ in.^2$

Area of frame with photo=120 square inches

Let x be the width of the frame, then we have

Length of frame with photo= 10+2x inches

Width of frame with photo =8+2x inches

Now, $(10+2x)(8+2x)=120$

$80+16x+20x+4x^2=120\\\Rightarrow\ 4x^2+36x-40=0\\\Rightarrowx^2+9x-10=0\\\(x-1)(x+10)=0\\\Rightarrow\ x=1,...........[text{Since length can not be negative so it cannot be -10}]$

Thus, dimension of frame = $(10+2(1))(8+2(1))=12\ in.\ by\ 10\ in.$