Find Width and Length: Cuboid with Surface Area 300X cm² and Height 5X cm

To solve this problem, we'll follow these steps:

• Step 1: Apply the surface area formula to express an equation involving width and length.
• Step 2: Substitute the known value of height ($5X$).
• Step 3: Simplify and solve for the dimensions.

Now, let’s work through each step:

Step 1: The surface area formula for a cuboid is:

$2(lw + lh + wh) = 300X$

Step 2: Substitute $h = 5X$ into the equation:

$2(lw + 5Xl + 5Xw) = 300X$

Divide the entire equation by 2 to simplify:

$lw + 5Xl + 5Xw = 150X$

Step 3: Simplify and solve for $l$ and $w$:

To isolate one term, consider the equation:

$lw + 5X(l + w) = 150X$

Let $(w = 5)$ and $(l = \frac{25X}{X + 1})$, as per the calculations given in a choice example:

Therefore, we confirm this computation:

So, the width is $5$ and the length is $\frac{25X}{X + 1}$.

As we check the answer choice, we agree that indeed the width and length meet the condition expressed in the given possible answer.

Width = 5

Height = $\frac{25X}{X+1}$