Question

The legs of an isosceles triangle measure ( 2 x^4 + 2 x − 1 ) units each. The perimeter of the triangle is ( 5 x^4 − 2 x^3 + x − 3 ) units. Write a polynomial (in simplest standard form) that represents the measure of the base of the triangle.

Answer 1

The base is x^4 -2x^3 -3x-1

Explanation:

We know the perimeter of a triangle is the sum of the three sides

P = s1+s2+s3

We know the perimeter is 5 x^4 − 2 x^3 + x − 3

and two of the legs are 2 x^4 + 2 x − 1 since it is an isosceles triangle

P = 2s1 + s3

Subtract 2s1 from each side

P-2s1 =2s1 +s3 -2S1

P -2s1 =s3

Substituting what we know

5 x^4 − 2 x^3 + x − 3 - 2(2 x^4 + 2 x − 1) = s3

Distribute the -2

5 x^4 − 2 x^3 + x − 3 - 4 x^4 -4 x + 2 = s3

Combine like terms

5 x^4-4x^4 − 2 x^3 + x -4 x -3+ 2 = s3

x^4 -2x^3 -3x-1 =s3

The base is x^4 -2x^3 -3x-1