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Question

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 ΔABC and ΔPQR

AB = PR = 5 cm

BC = PQ

AC = QR = 7 cm

Therefore, ΔABCΔPQR by SSS criterion.

Since perimeter = 18cm

AB + AC + BC = 18 cm,

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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