ABCD has area equal to 28cm.BC is parallel to AD.BA is perpendicular to AD.If BC=6cm and AD=8cm, then what is CD?
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Explanation:
the area, 28, is the area not just of the rectangular portion of the quadrilateral; it also includes the triangular portion. Let's call the height (the length of AB) 'h'. We can divide the picture into a rectangle, with a base of 6, and a right angled triangle, with a base of 2. We know that the area of the rectangle plus the area of the triangle is 28:
6*h + 2*h/2 = 28
7*h = 28
h = 4
You've also left off a square (^2) on the right side of the Pythagorean formula at the end of your solution. If we use h = 4, and b = 2 for the right angled triangle, we should have:
CD^2 = 4^2 + 2^2
CD^2 = 20
CD = root(20) = 2*root(5)
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