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construct a square when the sum of its diagonal and side is given

Can someone tell me construct a square when the sum of its diagonal and side is given.......
asked Jul 9, 2013 in Geometry Answers by NGU

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2 Answers

sins yu did NOT giv it, me duit: 1 side+diagonal=10... diagonal=root(2), so 1+root(2)=10... anser=10/[1+root(2)]... bout 10/2.1414213562373095048801688724209... leng av 1 side av square=4.669795588
answered Jul 9, 2013 by muneepenee
Assuming we're familiar with ways how to draw 2 lines bisecting each other perpendicularly, or how to prove a shape to be a square or 2 lines parallel, explanations for those things are omitted in here. Let the given length: sum of its diagonal and a side, be h. 1). Draw a horizontal and a vertical approx.3h long each. They bisect each other perpendicularly at their midpoint O. Let the left end of the hor. be K and the right end L, the upper end of the vert. M and the lower end N. 2). From O, draw an arc with radius h crossing OL at P, so OP=h. Also from O, draw an arc with radius approx.h/2 crossing ON at A and OL at C. Then draw 2 arcs with radius OA, one from A rightwards and the other from C crossing the 1st at B below C. 3). Connect A to B and B to C. The quadrilateral OABC is a  square.  From O thru B, draw a ray approx.2h long and label the lower end V. From B draw an arc with radius BA crossing BV at D. So OB : BD = √2 : 1. 4). Connect P to D. Extend AB crossing PD at E. From P, draw an arc leftwards with radius BE crossing OP at Q. Connect Q to B. Thus PD // QB, OQ : QP = OB : BD = √2 : 1. OQ is a  diagonal of a square asked and QP is a side of it. 5). From O, Draw an arc with radius QP crossing OP at R and OM at T. Draw 2 arcs with radius QP, one from R upwards and the other from T crossing the 1st at S above R.  Connect R to S and S to T. The quadrilateral ORST is the square asked. 6). Check if OS corresponds to OQ. Draw an arc from O with radius OS. The arc cuts across OP at Q. CKD. Therefore, the suare ORST is the one drawn using  given sum of its diagonal and a side.
answered Sep 30, 2013 by tokiokid70
edited Oct 16, 2013

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