We start by writing an equation using the information. Afterwards, we will rewrite it in standard form. Then, we will use factoring to solve it.
Writing Equation
Tina wants to reduce the width and the length of the photo by the same amount so that the area of the smaller photo is half of the original area.
After she resizes the photo, the width and the length will be x inches shorter.
w= 12-x & l = 16-x
Since the area is reduced to half the original area, we can write the equation below.
( 12-x)( 16-x) = 12 * 16/2
⇕
(12-x)(16-x)= 96
Rewriting Equation
To find the new dimensions, we need to solve for x. Before that, we will rewrite the equation in standard form.
Let's substitute the solutions and find possible dimensions.
w=12-x
l = 16-x
x=24
w=12-24= - 12
l = 16-24= - 8
x=4
w=12-4= 8
l = 16-4= 12
Since dimensions cannot be negative, the new photo is 8 inches by 12 inches.
Checking Our Answer
Checking Our Answer
Let's check if the area of the new photo is equal to half the original area. w=8 & l=12
Their product is equal to 96, half the original area.
8 * 12 =96 ✓
