Question

11/7 - isosceles and equilateral practice
possible points: 0.8
the length of the base of an isosceles triangle is x. the length of a leg is 4x - 6. the perimeter of the triangle is 51. find x.
x =

Explanation:

Step1: Write the perimeter formula for the isosceles triangle

An isosceles triangle has two equal legs. The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So, \(P=x + 2(4x - 6)\).

Step2: Substitute the value of the perimeter

Since \(P = 51\), we have the equation \(51=x+2(4x - 6)\).
First, expand the right - hand side: \(51=x + 8x-12\).

Step3: Combine like terms

Combine the \(x\) terms: \(51=(1 + 8)x-12\), which simplifies to \(51 = 9x-12\).

Step4: Solve for \(x\)

Add 12 to both sides of the equation: \(51 + 12=9x-12 + 12\), so \(63 = 9x\).
Then divide both sides by 9: \(x=\frac{63}{9}\).

Answer:

\(x = 7\)