Let's draw the given scenario to better understand the problem:
Let,
W = Width
L = Length
For us to be able to get the width of the television, we will be using the Pythagorean Theorem:
[tex]\text{ a}^2+b^2=c^2[/tex]But,
a = Width = W
b = Width + 8 inches = W + 8
c = 40 inches = 40
We get,
[tex]\text{ a}^2+b^2=c^2[/tex][tex]\text{ (W)}^2+(W+8)^2=(40)^2[/tex][tex]\text{ W}^2+W^2\text{ + 16W + 64 = 1,600}[/tex][tex]2W^2\text{ + 16W + 64 - 1600 = 0}[/tex][tex]2W^2\text{ + 16W - 1,536 = 0}[/tex][tex]\frac{2W^2\text{ + 16W - 1,536}}{2}\text{ = 0}[/tex][tex]W^2\text{ + 8W - 768 = 0}[/tex]a = 1, b = 8 and c = -768
Using the quadratic formula,
[tex]\text{ W = x = }\frac{\text{ -b }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}\text{ = }\frac{-8\text{ }\pm\text{ }\sqrt[]{(8)^2\text{ - 4(1)(-768)}}}{2(1)}[/tex][tex]\text{ x = }\frac{-8\text{ }\pm\text{ }\sqrt[]{64\text{ + }3,072}}{2}\text{ = }\frac{-8\text{ }\pm\text{ 56}}{2}\text{ = -4 }\pm\text{ 28}[/tex][tex]\text{ x}_1\text{ = -4 + 28 = 24 inches}[/tex][tex]\text{ x}_2\text{ = -4 - 28 = -32 inches}[/tex]A width should never be a negative value, therefore, the most probable width of the television is 24 inches.
Therefore, the answer is 24 inches.
