Question

a plot of land is in the shape of a triangle. if one side is x meters, a second side is (5x - 3) meters and a third side is (7x - 4) meters, express the perimeter of the lot as a simplified expression in x. the perimeter of the lot is ( ) square meters.

Explanation:

Step1: Recall the formula for perimeter

The perimeter \(P\) of a triangle is \(P = a + b + c\), where \(a\), \(b\), and \(c\) are the side - lengths. Here, \(a=x\), \(b = 5x-3\), \(c=7x - 4\). So, \(P=x+(5x - 3)+(7x-4)\).

Step2: Remove parentheses

Using the property \(a+(b + c)=a + b + c\), we get \(P=x + 5x-3+7x-4\).

Step3: Combine like terms

Combine the \(x\) - terms: \(x+5x + 7x=(1 + 5+7)x=13x\). Combine the constant terms: \(-3-4=-7\). So, \(P = 13x-7\).

Answer:

\(13x - 7\)