Question

A triangle has sides of 5x-1 and 3(x-2) and 2x+5. Determine a simplified expression for the perimeter.

Answer 1

Answer:

perimeter is sum of all the sides.

perimeter of triangle = sum of sides

perimeter= 5x-1 + 3(x-2) + 2x+5

perimeter = 5x -1 +3x -6 +2x +5

perimeter = 10 x -7 +5

perimeter = 10 x - 2

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Answer 2

Answer:-

$\red{\bigstar}$ Simplified expression $\large\leadsto\boxed{\rm\green{10x - 2}}$

• Given:-

A triangle has sides of 5x-1 , 3(x-2) and 2x+5.

• To Find:-

Simplified expression for the perimeter.

• Solution:-

• According to the question-

$\setlength{\unitlength}{1 cm}\begin{picture}\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\put(0,1.5){ \bf 5x-1 }\put(5,1.5){ \bf 3(x-2) }\put(2.5,-1){ \bf 2x+5 }\end{picture}$

We know,

$\pink{\bigstar}$ Perimeter of a triangle = Sum of all sides [a+b+c]

Hence,

→ $\sf P = (5x - 1) + 3(x - 2) + 2x + 5$

→ $\sf P = 5x - 1 + 3x - 6 + 2x + 5$

→ $\sf P = 5x + 3x + 2x - 1 - 6 + 5$

→ $\sf P = 10x - 7 + 5$

→ $\bf P = 10x - 2$

Therefore, simplified expression for perimeter is 10x - 2.