A flat screen television is sized depending on the length of the diagonal (ex: a 40 inch flat screen has a 40 inch diagonal ). If a 32 inch television has a width that is 5 inches longer than its length. Determine the dimensions of the television (using exponential applications)
Use Pythagoras ...
shorter side = x
longer side = x+5
diagonal = 32
x^2 + (x+5)^2 = 32^2
x^2 + x^2 + 10x + 25 - 1024 = 0
2x^2 + 10x - 999 = 0
by formula:
x = 19.99 or appr 20 or a negative
so the two sides are appr 20 inches by 25 inches
To determine the dimensions of the television, we can use the Pythagorean theorem and solve for the length and width.
1. Let the length of the television be represented by "x" inches.
2. The width of the television is 5 inches longer than its length, so it can be represented as "x + 5" inches.
3. According to the Pythagorean theorem, the square of the length plus the square of the width should be equal to the square of the diagonal.
Mathematically, this can be represented as: x^2 + (x + 5)^2 = 32^2.
Now, we can solve this equation to find the value of "x" (the length) and "x + 5" (the width) using exponential applications:
1. Expand the equation: x^2 + (x^2 + 10x + 25) = 1024.
2. Combine like terms: 2x^2 + 10x + 25 = 1024.
3. Rearrange the equation: 2x^2 + 10x + 25 - 1024 = 0.
4. Simplify: 2x^2 + 10x - 999 = 0.
At this point, we have a quadratic equation. We can solve it by factoring, using the quadratic formula, or by completing the square. In this case, let's use the quadratic formula:
1. The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).
In our case, a = 2, b = 10, and c = -999.
2. Substitute these values into the quadratic formula:
x = (-10 ± √(10^2 - 4(2)(-999))) / (2(2)).
Simplify this equation.
After solving for "x" (the length), substitute the value of "x" into "x + 5" (the width) to find the dimensions of the television.