Question

alza is designing a new logo for her company. the general design of the logo is shown below. qr is the midsegment of △mwp and mn is the midsegment of △jkl. if qr = 2.3 cm, what is the length of kl? kl = □ cm

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the length of a mid - segment of a triangle is half the length of the third side. In \(\triangle MWP\), \(QR\) is a mid - segment. Let the side parallel to \(QR\) be \(MW\). Then \(MW = 2QR\). Given \(QR=2.3\mathrm{cm}\), so \(MW = 2\times2.3 = 4.6\mathrm{cm}\).

Step2: Apply the mid - segment theorem again

In \(\triangle JKL\), \(MN\) is a mid - segment. The mid - segment \(MN\) is parallel to \(KL\). By the mid - segment theorem, \(KL = 2MN\). Since \(MN = MW\) (from the properties of the figure, as the mid - segments are related in a way that \(MN\) has the same length as \(MW\) when considering the overall structure of the composed triangles), then \(KL=2\times4.6\).

Answer:

\(4.6\)