Chapter 10.2, Problem 8CE

To determine

To describe: the construction of a square with perimeter equal to $AC.$ .

Explanation of Solution

Given information:

The given statement is “a square with perimeter equal to $AC.$ ”.

The procedure to construct of square:

• Consider the line segment $\overline{PQ}$ 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 and Y.
• With X and 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.

  

Hence, the construction of a square with perimeter equal to $AC.$