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The perimeter of the isosceles ΔABC with the base
BC is equal to 40 cm. Perimeter of the equilateral ΔBCD is 45 cm. Find BC and AB.

Respuesta :

WojtekR
ΔBCD is equilateral, so

|BC| = |CD| = |DA|

and

[tex]P=|BC|+|CD|+|DA|\\\\45=|BC|+|BC|+|BC|\\\\45=3\cdot|BC|\quad|:3\\\\|BC|=45:3\\\\\boxed{|BC|=15\text{ cm}}[/tex]

ΔABC is isosceles and

|AB| = |CA| (legs)

[tex]P=|AB|+|BC|+|CA|\\\\P=|AB|+|BC|+|AB|\\\\40=2\cdot|AB|+15\\\\40-15=2\cdot|AB|\\\\25=2\cdot|AB|\quad|:2\\\\\boxed{|AB|=12.5\text{ cm}}[/tex]
onyebuchinnaji

The length of BC is 15 cm and the length of AB is 12.5 cm.

The given parameters;

  • perimeter of isosceles ΔABC = 40 cm
  • base of the isosceles triangle = BC
  • Perimeter of the equilateral ΔBCD =  45 cm

An equilateral triangle has three equal sides and the length of each side is calculated as;

[tex]|BC| = |BD| = |CD| = \frac{45}{3} = 15 \ cm[/tex]

Thus, the length of BC is 15 cm.

An isosceles triangle has two equal sides and a third side of different length. This third side is usually the base of the triangle.

  • The base of the isosceles triangle = BC = 15 cm
  • The two remaining sides = AB and AC

[tex]|AB| = |AC| =\frac{Perimeter \ - \ |BC|}{2} = \frac{40 - 15}{2} = 12.5 \ cm[/tex]

Thus, the length of AB is 12.5 cm.

Learn more here: https://brainly.com/question/11296804

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