Question

1. in △abc, the points j, l, and w are mid - points. ab = 22 cm, bc = 13 cm, and ac = 14 cm. answer the following:

a. jl=

b. wl=

c. perimeter of △jl w=

Explanation:

Step1: Recall mid - point theorem

The line segment joining the mid - points of two sides of a triangle is parallel to the third side and half of its length.

Step2: Find \(JL\)

Since \(J\) and \(L\) are mid - points of \(AC\) and \(AB\) respectively, by the mid - point theorem, \(JL=\frac{1}{2}BC\). Given \(BC = 13\ cm\), so \(JL=\frac{13}{2}=6.5\ cm\).

Step3: Find \(WL\)

Since \(W\) and \(L\) are mid - points of \(BC\) and \(AB\) respectively, by the mid - point theorem, \(WL=\frac{1}{2}AC\). Given \(AC = 14\ cm\), so \(WL = 7\ cm\).

Step4: Find \(JW\)

Since \(J\) and \(W\) are mid - points of \(AC\) and \(BC\) respectively, by the mid - point theorem, \(JW=\frac{1}{2}AB\). Given \(AB = 22\ cm\), so \(JW = 11\ cm\).

Step5: Find the perimeter of \(\triangle JLW\)

The perimeter of \(\triangle JLW\) is \(P=JL + WL+JW\). Substituting the values: \(P = 6.5+7 + 11=24.5\ cm\).

Answer:

a. \(6.5\ cm\)
b. \(7\ cm\)
c. \(24.5\ cm\)