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The height of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Determine the length of the rectangle.
a. 20
b. 23
c. 22
d. 21
d. To determine the length of the rectangle, we will use the Pythagorean theorem. The width, a, is 20. The diagonal, c, is x + 8. The length, b, is x; a2 + b2 = c2; 202 + x2 = (x + 8)2. After multiplying the two binomials (using FOIL), 400 + x2 = x2 + 16x + 64. Subtract x2 from both sides; 400 = 16x + 64. Subtract 64 from both sides; 336 = 16x. Divide both sides by 16; 21 = x. If you select a, you incorrectly calculated the diagonal to be 28.
for all real numbers x, x 0
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