The width of a rectangular photograph is 5cm more than the height. The area is 80cm squared. Find the height of the photograph.
Student
To find the height of the photograph, we first need to set up an equation based on the given information.
Let's assume the height of the photograph is represented by 'h' cm. Since the width is 5 cm more than the height, we can represent the width as 'h + 5' cm.
The area of a rectangle is calculated by multiplying the length and the width. In this case, the area is given as 80 cm². So, we can set up the equation:
Area = Length × Width
80 = h × (h + 5)
To solve this equation, we can expand it:
80 = h² + 5h
Now, we have a quadratic equation. Let's rearrange the equation and set it equal to zero:
h² + 5h - 80 = 0
To factorize the quadratic equation, we need to find two numbers that multiply to -80 (-80 = -8 × 10) and add up to 5. The numbers are 10 and -8:
(h + 10)(h - 8) = 0
Setting each factor equal to zero and solving for 'h', we get two possible heights:
h + 10 = 0 or h - 8 = 0
h = -10 or h = 8
Since height cannot be a negative value in this context, we discard h = -10.
Therefore, the height of the photograph is h = 8 cm.
width * height = area
Insert the two known values and solve for the remaining value.