In rectangle ABCD shown, the length of side AB is greater than the length of side BC, the length of line segment DE is m, and the length of line segment BF is n.Quantity AThe length of diagonal BD (not shown)Quantity Bm + n
Answer(s): C
The diagonal BD is fixed by rectangle dimensions:The segments m = DE and n = BF are altitudes (perpendicular distances) from D and B to the opposite diagonal AC.So m + n is the sum of distances from both opposite vertices (D and B) to diagonal AC.In a rectangle, if you drop perpendiculars from two opposite vertices onto the other diagonal, the sum of those perpendiculars = the length of that diagonal.That is DE + BF = BDSo, m + n = BD
1 foot = 12 inches l yard = 3 feet1 mile = 5,280 feetApproximately how many cubic yards of asphalt are needed to cover a level road that is mile long and 24 feet wide with a layer of asphalt that is 4 inches thick?
Answer(s): A
Convert to feetLength:Width:24 ftThickness:Volume in cubic feet = length × width × thickness:Convert to cubic yards:1 yard = 3 feet 1 cubic yard = 33 = 27 cubic feet782 800 yd3
If the length of one of the diagonals of quadrilateral Q is 10, which of the following values could be the perimeter of Q?Indicate all such values.
The diagonal of length 10 divides the quadrilateral into two triangles. In each triangle, the sum of its two other sides must exceed 10, so together the four sides must total more than 20.
If the area of the triangular region above is , what is x in terms of y?
A circular pond has a diameter of 20 feet. A fence is to be built in the shape of a circle to surround the pond. If the pond and the circular region enclosed by the fence have the same center, and if the shortest distance between the fence and the edge of the pond is 10 feet, approximately what will he the length of the fence, in feet?
Answer(s): D
Since the pond's radius is 10 feet and the fence is 10 feet farther out, the radius of the fence is:10 (pond radius) + 10 (gap) = 20 feetCircumference = 2 × × radius= 2 × × 202 × 3.14 × 20 125.6 feet 126 feet
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