Question

In a set of picture frames, frame 1 has a length that is 5 inches longer than its width, w, and frame 2 has the same length as frame 1, but is 2 inches wider than frame 1. The area of frame 2 is 28 square inches more than the area of frame 1. Express these conditions into mathematical formula.

Answer 1

Answer: The mathematical formula would be

$(w+5)\times (w+2)-(w+5)(w)=28$

Step-by-step explanation:

Let the width of the frame 1 be 'w'.

Let the width of the frame 2 be 'w+2'.

Let the length of frame 1 be 'w+5'.

Let the length of frame 2 be 'w+5'.

Since the area of frame 2 is 28 square inches more than the area of frame 1.

According to question, it becomes,

$\text{Area of frame 2 - Area of frame 1}=28\\\\(w+5)\times (w+2)-(w+5)(w)=28\\\\(w^2+10+7w)-(w^2+5w)=28\\\\w^2+10+7w-w^2-5w=28\\\\2w+10=28\\\\2w=28-10\\\\2w=18\\\\w=\dfrac{18}{2}\\\\w=9$

Hence, the mathematical formula would be

$(w+5)\times (w+2)-(w+5)(w)=28$