Q4. - Algebra 1

Question

Find the value of x so that the figures have the same perimeter.

F 1.5   G 2      H 3.2   J 4

Step-by-Step Solution

Answer

The value of x so that the figures have the same perimeter is 2. So, the correct option is G.

Step 1. State the formula.

The perimeter of a rectangle is given as $2\left(l+w\right)$, where $l$ is the length of the rectangle and $w$ is the width of the rectangle.

Step 2. List the given data.

From the figure, the length of the first rectangle is $6$ units and the width of the first rectangle is $x$ units. Then, the perimeter of the first rectangle is $2\left(6+x\right)$ units.

 

Similarly, from the given figure, the length of the second rectangle is $x$ units and the width of the second rectangle is $2x+2$ units. Then, the perimeter of the second rectangle is $2\left(x+2x+2\right)$ units.

Step 3. Formulate the equation.

It is given that the figures have the same perimeter. Then, the perimeters of the first and second rectangle are equal. So, “$2\left(6+x\right)=2\left(x+2x+2\right)$”.

 

This is the required equation.

Step 4. Solve the obtained equation.

Solving,

$2\left(6+x\right)=2\left(x+2x+2\right)$  (Given equation)

$\frac{2\left(6+x\right)}{2}=\frac{2\left(x+2x+2\right)}{2}$  (Divide both sides by 2)

$6+x=3x+2$  (Simplify)

$6+x-3x=3x+2-3x$  (Subtract $3x$ from both sides)

$6-2x=2$  (Simplify)

$6-2x-6=2-6$  (Subtract 6 from both sides)

$-2x=-4$  (Simplify)

$\frac{-2x}{-2}=\frac{-4}{-2}$  (Divide both sides by $-2$)

$x=2$  (Simplify)

So, $x=2$ is the solution of the given equation.

Step 5. Interpret the obtained solution.

It was assumed that the perimeters of both figures are equal. This assumption led to the obtained solution $x=2$.

 

Thus, the value of x so that the figures have the same perimeter is 2.