Question

5 the perimeter of a rectangle can be found using the expression: 2(4\sqrt{3y}) + 2(5\sqrt{12y}) which expression represents the perimeter in simplest form? a 18\sqrt{6y} b 28\sqrt{3y} c 8\sqrt{3y}+10\sqrt{12y} d 18y\sqrt{3}

Explanation:

Step1: Expand the given expression

$2(4\sqrt{3y})+2(5\sqrt{12y}) = 8\sqrt{3y}+10\sqrt{12y}$

Step2: Simplify $\sqrt{12y}$

$\sqrt{12y}=\sqrt{4\times3y}=2\sqrt{3y}$

Step3: Substitute the simplified form

$8\sqrt{3y}+10\sqrt{12y}=8\sqrt{3y}+10\times2\sqrt{3y}=8\sqrt{3y} + 20\sqrt{3y}$

Step4: Combine like - terms

$(8 + 20)\sqrt{3y}=28\sqrt{3y}$

Answer:

B. $28\sqrt{3y}$