# One of the legs of a right-angled triangle is 15 cm and the projection of the other leg onto

One of the legs of a right-angled triangle is 15 cm and the projection of the other leg onto hepotinuse is 16 cm. Find the pyrimeter of the triangle.

AB – leg of a right-angled triangle; AB = 15 cm;
KS – projection of the AC leg onto the BC hypotenuse; CS = 16 cm;
By the Pythagorean theorem: AC² = BC² – AB²;
According to the formula for the relationship between the leg and its projection onto the hypotenuse:
AC² = BC * KC;
BC² – AB² = BC * KC;
BC² – 16 * BC – 225 = 0;
BC = 8 + 1/2 √ (16² + 4 * 225) = 8 + 1/2 √ 1156 = 8 +17 = 25 (cm);
AC² = 25 * 16 = 400 (cm²); AC = √400 = 20 (cm);
P = AB + BC + AC = 15 + 25 + 20 = 60 (cm).

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