# exercise#1) Suppose a rectangular patch of land is set aside out in…

exercise#1) Suppose a rectangular patch of land is set aside out in… exercise#1) Suppose a rectangular patch of land is set aside out in the country. From North to South, it measures L meters, and from East to West, it measures 30 meters less than the North-South dimension. But now since this patch is being used to grow a secret ingredient that Hulk likes to mix into his protein shake, the grower hides the patch with a tree strip all the way around. The Northern border tree strip is 8m wide, the Southern border 6m wide, and the Eastern and Western borders are each 5m wide. They are extended to make a perfect rectangle. (i) Draw a sketch of the configuration described above. Be sure you label all dimensions, including UNITS, and of course, use a straight edge. Use two colors. (ii) Find an expression, in terms of L, for the area of the field planted with the mystery ingredient. Be sure to include UNITS. (iii) Do the same as in (ii), for the area planted in trees. (iv) Write a complete English sentence that describes what you found in (ii) and (iii). (v) Now suppose it turns out that the area planted in trees is 80m2 less than the area planted in Hulk’s secret ingredient. Write an equation that expresses this fact. (vi) Show how to solve the equation from (v) to yield two possible values for L. (vii) Only one of the two values from (vi) makes sense. Explain which one is therefore the solution, and why. (viii) Now draw a new figure, with all the dimensions filled in. Again be sure to label with UNITS. Then tell us the areas of both the planted rectangle and of the tree strips. Answer this in a complete sentence. (ix) Finally HULK builds a fence around the perimeter of the tree strip! What length of fencing must he use to surround the property? Be sure to finish by explaining your result in a complete English sentence. exercise #2)   Consider the points A(0,8), B(3,0), C(-7,0), D(0,1). (i) Using graph paper and straight edge, sketch lines AB and CD. SPREAD OUT THE SCALE!! Otherwise, your sketch will be too small to label properly. (ii) Find the equation of each line, and it with its equation. (iii) Find the intersection E of the two lines in (ii). Use fractions, NEVER DECIMALS. Label this point clearly on your sketch. (iv) Shade triangle BCD. Then find its exact area in fractions. (Use the formula for area of a triangle, which you all know very well!) (v) Next, sketch the PERPENDICULAR BISECTOR of segment CD. Label clearly the midpoint F, with coordinates. (vi) Find the equation of the line in (v), and label it on your sketch. Again, work in fractions, not decimals  Math Algebra MATH 115 Share (0)

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