Question

triangle abc is congruent to triangle xyz. in \\( \triangle abc \\), \\( ab = 12 \mathrm{cm} \\) and \\( ac = 14 \mathrm{cm} \\). in \\( \triangle xyz \\), \\( yz = 10 \mathrm{cm} \\) and \\( xz = 14 \mathrm{cm} \\).
what is the perimeter of \\( \triangle abc \\)?
\\( 36 \mathrm{cm} \\)
\\( 38 \mathrm{cm} \\)
\\( 40 \mathrm{cm} \\)
\\( 50 \mathrm{cm} \\)

Explanation:

Step1: Use congruent triangles property

Since \(\triangle ABC\cong\triangle XYZ\), corresponding sides are equal. So \(AC = XZ = 14\mathrm{cm}\), \(AB=XY = 12\mathrm{cm}\), \(BC = YZ=10\mathrm{cm}\).

Step2: Calculate the perimeter

The perimeter \(P\) of \(\triangle ABC\) is \(P=AB + BC+AC\). Substitute \(AB = 12\mathrm{cm}\), \(BC = 10\mathrm{cm}\), \(AC = 14\mathrm{cm}\) into the formula: \(P=12 + 10+14\).

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Answer:

36 cm