The width of a rectangular photograph is 5cm more than the height. The area is 80cm squared. Find the height of the photograph.
should have been
h(h + 5) = 80
h^2 + 5h - 80 = 0
using formula
h = (-5 ± √ 345)/2
= 6.78 or some negative number
so height is 6.78
width = 11.78
area = 6.78x11.78 = 79.87
don't know what accuracy you needed in the answer.
let the height be h
then width is h+5
solve h(x+5) = 80 as a quadratic
but how do u solve h(x+5)=80
i have never come across ones like these.
To find the height of the photograph, we can use algebraic equations based on the given information.
Let's say the height of the photograph is represented by "h" cm.
According to the given information, the width of the photograph is 5 cm more than the height, which means the width would be (h + 5) cm.
The area of a rectangle can be calculated by multiplying its length (in this case, the width) by its width (in this case, the height).
So we have the equation:
Area = Length * Width
Substituting the given information:
80 = h * (h + 5)
Now let's solve this equation step by step:
1. Expand the equation:
80 = h^2 + 5h
2. Rearrange the equation:
h^2 + 5h - 80 = 0
3. Factorize or use the quadratic formula to solve for h:
Since this equation doesn't factorize easily, we'll use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 1, b = 5, and c = -80.
Using the quadratic formula, we get:
h = (-5 ± √(5^2 - 4*1*(-80))) / (2*1)
Simplifying further:
h = (-5 ± √(25 + 320)) / 2
h = (-5 ± √345) / 2
4. Calculate the two possible values for h:
Using the positive square root:
h = (-5 + √345) / 2 ≈ 6.27
Using the negative square root:
h = (-5 - √345) / 2 ≈ -11.27
Since the height cannot be negative, we discard the negative solution.
Therefore, the height of the photograph is approximately 6.27 cm.