A square blue rug has a red square in the center. The side length of the red square is x inches. The width of the blue band that surrounds the red square is 10 in. What is the area of the blue band?

Step-by-step explanation:

Length of the Blue Square = 10 inch

Length of the Red Square = x inch

Area of a Square =

The Area of the Blue Band = Area of the Blue Square - Area of the Red Square

The area of the blue band is

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.