Consider the figure below:

If AB = 5 cm; QR = 7cm; then find the value of AC (in cm.), if the perimeter of $△$ ABC is 18cm.

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Solution

In the given figure:

In $Δ A B C a n d Δ P Q R$

AB = PR = 5 cm

BC = PQ

AC = QR = 7 cm

Therefore, $Δ A B C ≅ Δ P Q R$ by SSS criterion.

Since perimeter = 18cm

$\Rightarrow$ AB + AC + BC = 18 cm,

$\Rightarrow$ BC = 18 - 5 - 7 = 6 cm.

Therefore,
AB = PR = 5 cm

BC = PQ = 6 cm

AC = QR = 7 cm
So, the answer is 7 cm.

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