The length of the hypotenuse, which is the leg times 2 \sqrt 3 2 meters, and each leg is 3 meters. This method takes more time than the square method but is elegant and does not require measuring. Strike two arcs, one on the line segment and one on the perpendicular bisectorĬonnect the intersections of the arcs and segments ABC A B C is a right triangle with mA 90 m A 90, AB AC A B A C and mB mC. Each right triangle has an angle of ½, or in this case (½) (120) 60 degrees. Draw a line down from the vertex between the two equal sides, that hits the base at a right angle. This triangle is also called a 45-45-90 triangle (named after the angle measures). Divide the isosceles into two right triangles. Reset the compass with the point on the intersection of the two line segments and the span of the compass set to your desired length of the triangle's leg A right triangle with congruent legs and acute angles is an Isosceles Right Triangle. Use the straightedge to draw the perpendicular bisector by connecting the intersecting arcs If Side 1 was not the same length as Side 2 then the angles would have to be different and it wouldnt be a 45 45 90 triangle. Use the compass to construct a perpendicular bisector of the line segment by scribing arcs from both endpoints above and below the line segment this will produce two intersecting arcs above and two intersecting arcs below the line segment Open the compass to span more than half the distance of the line segment The student earned 1 of the 2 integrand points and is not eligible for the answer point. The student presents a correct expression for the length of one of the sides of the triangle, but presents an incorrect expression for the length of the other side. Choice D is incorrect and may result from conceptual or calculation errors.You can also construct the triangle using a straightedge and drawing compass:Ĭonstruct a line segment more than twice as long as the desired length of your triangle's leg attempts to work with the area of a cross section involving an isosceles right triangle. This is the length, in inches, of the hypotenuse. Therefore, the length, in inches, of one leg of the isosceles right triangle is 47 2.Ĭhoice A is incorrect and may result from conceptual or calculation errors. This is equivalent to l = 94 2 2, or l = 47 2. Applying the distributive property to the numerator and to the denominator of the right-hand side of this equation yields l = 188 - 94 2 + 188 2 - 94 4 4 - 2 2 + 2 2 - 4. Rationalizing the denominator of the right-hand side of this equation by multiplying the right-hand side of the equation by 2 - 2 2 - 2 yields l = 94 + 94 2 2 - 2 2 + 2 2 - 2. I would be so grateful if someone could help. Dividing both sides of thisequation by 2 + 2 yields l = 94 + 94 2 2 + 2. This problem that Ive encountered is very difficult, and I tried using the formula of the area of an isosceles triangle, but I dont know where to go from there. Factoring the left-hand side of this equation yields l + l + l 2 = 94 + 94 2, or 2 + 2 l = 94 + 94 2. It's given that the perimeter of the triangle is 94 94 2 + inches. Therefore, the perimeter of the isosceles right triangle is l + l + l 2 inches. The perimeter of a figure is the sum of the lengths of the sides of the figure. It follows that the length of the hypotenuse is l 2 inches. Let l represent the length, in inches, of each leg of the isosceles right triangle. In an isosceles right triangle, the two legs have equal lengths, and the length of the hypotenuse is 2 times the length of one of the legs. It's given that the right triangle is isosceles. What is the length, in inches, of one leg of this triangle?Ĭhoice B is correct. An isosceles right triangle has a perimeter of 94 + 94 2 inches.
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