An architect presents a 3 inch wide by 4 inch deep by 3 inch tall model of a new central campus dorm . If the final building foundation is 126 feet wide how deep (in feet) will the building be?

Building depth = 168 ft

Step-by-step explanation:

we must find the relationship (scale) of the model with respect to the building .

wide-m (model) = 3 in

deep-m(model) = 4 in

wide-b (building) = 126 feet

deep-b(building) = x

the measures must be standardized

let's convert feet to inches

12 in      →   1 feet

3   in     →   ?,   then

3 in → 0.25 feet and 4 in → 1/3 feet

now deep-m = x

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.