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The diagonal of a rectangle does not provide enough information to determine the length of the rectangle.
Let L be any real number such that 32/sqrt(2) < L < 32.
let B = sqrt(32^2 - L^2)
Since L < 32 the above square root exists, and since L > 32/sqrt(2), B < L.
So the rectangle with sides of L and B will have a diagonal of 32 inches.
But L is any of an infinite number of possible real numbers. Therefore there are infinitely many possible solutions.
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The length of the rectangle below is 26.63 inches. If the diagonal makes an angle of 42.6 and ordm with this side find the measure of the width of the rectangle rounded to the nearest tenth of an inch?
The diagonal creates a right angled triangle with one pair of long and short sides - the diagonal is the hypotenuse. We know the angle between the long side (adjacent) and hypotenuse as 42.6°; We want to find the length of the short (width) side (opposite). We can use the Tan ratio: tan = opposite/adjacent → opposite = adjacent × tan → width = 26.63 in × tan 42.6° = 24.487... in → width is 24.5 inches to the nearest tenth of an inch.
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A square inch is a measure of area. The area could have any shape but for simplicity consider squares and rectangles where the area is given by the product of length and width, lxw. The length and the width are linear measurements. You can assign any values you want to the length and width and their product will be an area. A square with sides of 1 inch will have an area of one square inch. A rectangle whose length is 2 inches and width 1/2 inch will also have an area of one square inch.
