Question

question 1 a rectangular room is 2 times as long as it is wide, and its perimeter is 30 meters. find the dimension of the room. the length is : meters and the width is meters.

Explanation:

Step1: Set width as $x$

Let the width of the room be $x$ meters. Then the length is $2x$ meters.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$. Here $P=30$, $l = 2x$ and $w=x$. So $30=2(2x + x)$.

Step3: Simplify the equation

First simplify the right - hand side: $2(2x + x)=2\times3x = 6x$. So the equation becomes $6x = 30$.

Step4: Solve for $x$

Divide both sides of the equation $6x = 30$ by 6: $x=\frac{30}{6}=5$.

Step5: Find the length

Since the length $l = 2x$, substitute $x = 5$ into it, we get $l=2\times5 = 10$.

Answer:

Length: 10 meters, Width: 5 meters