Line BD is perpendicular to the plane of triangle ABC. it is known that BD = 9 cm, AC = 10 cm

| June 15, 2021 | education

Line BD is perpendicular to the plane of triangle ABC. it is known that BD = 9 cm, AC = 10 cm, BC = BA = 13 cm. Find the area of the triangle ACD.

Given: BD = 9cm,
AC = 10cm,
BC = ВA = 13cm,
Find: S – triangle ACD.
Decision.
Triangle ABC is isosceles with equal sides BC and BA, which are projections of oblique AD and DC. If the projections of these oblique are equal, then the oblique AD = DC themselves are equal. Hence we have that triangle ADC is isosceles. Let’s draw the height DK, which is also the median for the opposite side, so KС = 1 / 2АС = 1/2 * 10 = 5 (cm). From the triangle DCB by the Pythagorean theorem DC ^ 2 = BC ^ 2 + BD ^ 2, DC ^ 2 = 13 ^ 2 + 9 ^ 2 = 250, DC = √250 = 5√10 (cm). From the triangle DKC leg DK ^ 2 = DC ^ 2-KC ^ 2, DK ^ 2 = (5√10) ^ 2-5 ^ 2 = 250-25 = 225, DK = √225 = 15 (cm).
S = 1 / 2DK * AC = 1/2 * 15 * 10 = 75 (see sq.)



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