Question

solve for the following using the theorems/properties of a square.
ml = _ ne = _
perimeter of jklm = _ feet
area of jklm = _ ft²
if mk = 17 ft, then ol = _
m∠oml = _ m∠jok = _
m∠jml = _ m∠okl = _

Explanation:

Step1: Properties of a square

In a square, all sides are equal. So \(ML = 12\) (since \(JK = 12\) and \(JKLM\) is a square).

Step2: Perimeter of a square

The formula for the perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Here \(s = 12\), so \(P=4\times12 = 48\)

Step3: Area of a square

The formula for the area of a square is \(A=s^{2}\). Here \(s = 12\), so \(A = 12^{2}=144\)

Step4: Diagonals of a square

The diagonals of a square bisect each other. If \(MK = 17\) (diagonal), then \(OL=\frac{MK}{2}=\frac{17}{2}=8.5\)

Step5: Angles in a square

• In a square, the diagonals are perpendicular bisectors of each other. \(\angle JOK = 90^{\circ}\)
• In right - triangle \(OML\), \(\angle OML = 45^{\circ}\) (because the diagonals of a square bisect the vertex angles, and the vertex angle of a square is \(90^{\circ}\))
• \(\angle JML=45^{\circ}\) (diagonal bisects the vertex angle of the square)
• In right - triangle \(OKL\), \(\angle OKL = 45^{\circ}\)

Answer:

\(ML = 12\), \(NE\) (assuming \(NE\) is a typo, if it's related to side length it should be \(12\)), Perimeter of \(JKLM=48\) feet, Area of \(JKLM = 144\) \(ft^{2}\), If \(MK = 17\) ft, then \(OL = 8.5\), \(m\angle OML=45^{\circ}\), \(m\angle JOK = 90^{\circ}\), \(m\angle JML=45^{\circ}\), \(m\angle OKL = 45^{\circ}\)