Calculate the perimeter of the rectangle if the side is 24cm and the diagonal is 25cm.

univerkov | March 19, 2021 | education

Given: ABCD – rectangle, AD = 24 cm, AC = 25 cm – diagonal.

Find: PABCD -?

Decision:

Consider Δ ACD: ∠ADС = 900, hence Δ ACD is rectangular. By the Pythagorean theorem: AC^2 = CD^2 + AD^2;

25^2 = CD^2 + 24^2;

CD^2 = 625 – 576 = 49;

СD = √49 = 7 (cm);

PABCD = 2 * CD + 2 * AD = 2 * 7 + 2 * 24 = 14 + 48 = 62 (cm).

Answer: 62 cm.

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