Two isosceles triangles have equal angles opposite the bases. In one of the triangles, the side and the height

| September 3, 2021 | education

Two isosceles triangles have equal angles opposite the bases. In one of the triangles, the side and the height drawn to the base is 5 cm 4 cm.Find the perimeter of the second triangle if its side is 15 cm.

Let us designate the data by the condition as triangles ABC and A1B1C1, in the first triangle the height BH is known.
In the right-angled triangle ABN we find the leg AN (according to the Pythagorean theorem):
AH = √ (AB² – BH²) = √ (25 – 16) = √9 = 3 (cm).
We find the base of the AC (BH – height, bisector, median):
AC = 2 * AH = 6 (cm).
By condition, two isosceles triangles have an equal angle between the lateral sides. This is the first sign of the similarity of isosceles triangles. From the similarity of the triangles, the aspect ratio follows:
AB / A1B1 = AC / A1C1 = 5/15 = 6 / A1C1.
A1C1 = 18 (cm).
Find the perimeter of the triangle A1B1C1
P = 15 + 15 + 18 = 48 (cm).
Answer: the perimeter is 48 cm.



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