In an isosceles triangle ABC, the lateral side is 16.4 in. From point D, which is the midpoint of the lateral side AB
| March 4, 2021 | education
In an isosceles triangle ABC, the lateral side is 16.4 in. From point D, which is the midpoint of the lateral side AB, a perpendicular is drawn. This perpendicular intersects side BC at point E. The perimeter of triangle AEC is 26.9 inches. Find the AC side.
In triangle ABE, the height DE divides AB in half, therefore, DE is also the median of triangle ABE. Then triangle ABE is isosceles, AE = BE.
Let the length AE = BE = X cm. Then the length CE = BC – BE = (16.4 – X) dm.
The perimeter of the triangle AEC is equal to: Raes = AE + EC + AC = 26.9 dm.
X + (16.4 – X) + AC = 26.9 dm.
AC = 26.9 – 16.4 = 10.5 cm.
Answer: The length of the AC side is 10.5 cm.
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