The floor of a conference hall can be covered completly with tiles. its length is 36ft. longer than its width. the area of the floor is less than 2040square ft. how would you represent the with of the floor? how about its lenght? what mathematical sentence would represent the given situation? what are the possible dimensions of the floor? how about the possible areas of the floor? would it be realistic for the floor to have an area of 144sq. ft? explain your answer.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.