High school algebra . gle is 1161 square yards, and its perimeteris 140 yards. Find the dimensions. 33. Solve 1 + 1 == -3, i - i - -03. X y x^ y~ 34. The sum of a number of two digits and the number formed byreversing the digits is 121. The product of the digits is 28. Find thenumber. 35. Find the sides of a right-angled triangle whose perimeter is24 inches and whose area is 24 square inches. 36. Prove, algebraically, that if two rectangles have equal areasand equal perimeters, they are equal in all respects. 37. Solve a;2+a-2/+i/2=7-75, x^—xy-\-y^=5-2ii. 38. What must be the dimensions of a r
High school algebra . gle is 1161 square yards, and its perimeteris 140 yards. Find the dimensions. 33. Solve 1 + 1 == -3, i - i - -03. X y x^ y~ 34. The sum of a number of two digits and the number formed byreversing the digits is 121. The product of the digits is 28. Find thenumber. 35. Find the sides of a right-angled triangle whose perimeter is24 inches and whose area is 24 square inches. 36. Prove, algebraically, that if two rectangles have equal areasand equal perimeters, they are equal in all respects. 37. Solve a;2+a-2/+i/2=7-75, x^—xy-\-y^=5-2ii. 38. What must be the dimensions of a rectanfrular field containing7J acres, if the greatest distance from any point in its boumlary toany other point is 50 rods ? 288 ALUEBKA 39. The sum of the radii of two circles is 8 inches and the sum oftheir areas is | of the area of a circle whose radius is 9 inches. Whatare their radii ? 40. What must be the length of a rectangular field that containsa square rods and which can be enclosed by a fence b rods 199. Graphical Methods. What is the distance of thepoint P(4, 3) from the origin 0 ? Since OP^=OM^-^MP^, . OP2:^42+32=25, .-. OP =5. If any point {x^y) is the samedistance from the origin that P is,then the point {x,y) must lie ona circle whose radius is 5 andwhose centre is 0. But thesquare of the distance of the point{x,y) from the origin is x^-\-y^, :. a;2+?/2=25. It is thus seen that the equation x^-{-y^=25 represents acircle whose radius is 5 and whose centre is the origin. Similarly, x^ + y^—lQ, x^+y^=lOO, x^ + y^=l8, represent circleswith the origin as centres and whose radii respectively are 4, 10, VlS. It is seen that it is a simple matter to draw the graph ofthe equation of the circle in the form z^-\-y^=r^. All werequire to do is to describe with the compasses a circle whosecentre is the origin and whose radius is r. When the radius is a surd as in x^-\-y^=lS, it is simplerto find a pair of values of x and y which satisfy the x=3, 2/=3
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Keywords: ., bookauthorcr, bookcentury1900, bookdecade1910, booksubjectalgebra
