Let [tex]x[/tex] be the width of the original rectangle. Since the length of the rectangle is 8 more than the width, [tex]x+8[/tex] will be the length of our rectangle.
We know that two equal triangles were cut form the rectangle to make the coffee table top, and that the base and height of those triangles is [tex] \frac{1}{4} [/tex] of the width of the original rectangle. Since the width of the original rectangle is [tex]x[/tex], the base and the height of both triangles will be [tex] \frac{1}{4} x[/tex].
We also know that the the area of the finished top is 352, so the sum of the areas of the triangles will 352.
Now, the formula to find the area of a triangle is: [tex]A= \frac{1}{2} bh[/tex]
where
[tex]A[/tex] is the area of the triangle
[tex]b[/tex] is the base of the triangle
[tex]h[/tex] is the height of the triangle
We know that [tex]b= \frac{1}{4}x [/tex] and [tex]h= \frac{1}{4} x[/tex]. Lets replace those values in our formula:
[tex]A= (\frac{1}{2})( \frac{1}{4}x)( \frac{1}{4}x) [/tex]
Notice that we have two triangles; therefore we need to multiply by 2 the area:
[tex]A=2[(\frac{1}{2} )( \frac{1}{4} x)( \frac{1}{4} x)][/tex]
Since we know that the area of both triangles is 352, [tex]A=352[/tex]:
[tex]352=2[(\frac{1}{2} )( \frac{1}{4} x)( \frac{1}{4} x)][/tex]
[tex]352=( \frac{1}{4} x)( \frac{1}{4} x)[/tex]
[tex]352= \frac{1}{16} x^2[/tex]
[tex]x^2=(352)(16)[/tex]
[tex]x^2=5632[/tex]
[tex]x= \sqrt{5632} [/tex]
[tex]x=75.05[/tex]
We can conclude that the width of our rectangle is [tex]75.05[/tex] and its length is [tex]75.05+8=83.05[/tex].
