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A frame measuring 9 units by 11 units will have an exact area of 99 units.

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17y ago

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The outside of a picture frame measures 8 in by 11 in 54in2 of the picture shows find the thickness of the frame?

To find the thickness of the frame, we start by determining the dimensions of the picture itself. The area of the picture is 54 in², and since the outside dimensions of the frame are 8 in by 11 in, we can set up the equation: Let the thickness of the frame be ( x ). Then the dimensions of the picture are ( (8 - 2x) ) by ( (11 - 2x) ). Setting up the equation: [ (8 - 2x)(11 - 2x) = 54 ] Expanding and simplifying gives us: [ 88 - 22x - 16x + 4x^2 = 54 ] [ 4x^2 - 38x + 34 = 0 ] Using the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) with ( a = 4, b = -38, c = 34 ), we find ( x ). Solving this results in ( x \approx 1 ) inch. Thus, the thickness of the frame is approximately 1 inch.