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

Video Solution

Solution Steps

00:00 Suggest options for box length and width

00:04 Use formula to calculate box surface area

00:07 Substitute appropriate values according to the data and solve for L and W

00:21 Simplify what's possible

00:42 Extract common factor from parentheses

00:49 Isolate the unknown L

01:05 Try setting box width (W) equal to 5

01:12 Substitute 5 in equation for every unknown W

01:36 Factorize 125 into factors 5 and 25

01:39 Extract common factor from parentheses

01:42 Simplify what's possible

01:49 This is length L when width W equals 5

01:52 And this is the solution to the problem

Step-by-Step Solution

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