Question

Describe how you would construct each of the following:

A square whose perimeter equals $\overline{AC}$ .

Short answer

The construction of a square with perimeter equal to$\overline{AC}$

Step-by-step solution

Step 1. Given information.   

The given statement is “a square with perimeter equal to $\overline{AC}$”.

Step 2. Concept used.

The perimeter of square is sum of all side.

Step 3. Construction.

The procedure to construct square:

• Consider the line segment $\overline{PQ}\subset$with length equal to$\frac{1}{4}\overline{AC}$.

• Using $Q$as centre draw two arcs of same radii that intersects the line$\overline{PQ}$at two

points$X \&Y$.

• With $X \&Y$as centers and suitable radius, draw two arcs that intersect at point$Z$.

• Draw the line$\overline{QZ}$.

• Using the length of$\overline{PQ}$with centre$Q$,draw an arc on the line $\overline{QZ}$. Label the

point $R$.

• Using the same length with centre $P,R$and draw two arcs. Intersecting point is$S$.

• Join $\overline{PS}$and $\overline{RS}$.

• Obtain the square$PQRS.$

The construction is shown below.

Therefore, the construction of a square with perimeter equal to$\overline{AC}$