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Triangle ABC is an isosceles triangle with vertex angle B, AB=5x-28, AC=x+5, and BC= 2x+11. How do you find the length of the base?

Answer 1

Eva Abramson

Since B is the isosceles triangle's vertex angle, AB = BC and AC is its base side.

Given that AB = BC

So, #5x - 28 = 2x + 11#

#5x - 2x = 28 + 11#

#3x = 39#

#x = 39/3 = 13#

AC = #x + 5# = 13 + 5 = 18

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Answer 2

Isaiah Anthony

Given: Triangle ABC is an isosceles triangle with vertex angle B.

We have: [ AB = 5x - 28 ] [ AC = x + 5 ] [ BC = 2x + 11 ]

In an isosceles triangle, the lengths of the two equal sides are the same. So, in triangle ABC, AB = AC.

[ 5x - 28 = x + 5 ]

Solving for ( x ):

[ 5x - x = 28 + 5 ] [ 4x = 33 ] [ x = \frac{33}{4} ]

Now, substitute ( x ) back into the expression for the length of the base:

[ BC = 2x + 11 ] [ BC = 2\left(\frac{33}{4}\right) + 11 ] [ BC = \frac{66}{4} + 11 ] [ BC = \frac{66 + 44}{4} ] [ BC = \frac{110}{4} ] [ BC = 27.5 ]

So, the length of the base (BC) is 27.5 units.

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