The problem you've shared involves a three-dimensional geometric shape, specifically a triangular prism-like structure.

Given Information:

• The length of sides $AB$ and $AC$ are equal (denoted as $l$).
• The base $BC = b$.
• The perpendicular height $AD = 2.5$ meters.
• The ratio of the length of the sides $l$ to the length of the base $BC$ is given as $4:3$.

Problem 1.1:

You are asked to determine the length of the sides $l$ in meters.

Step-by-step Solution:

From the ratio provided, we can say: $\frac{l}{b} = \frac{4}{3}$

Let $l = 4x$ and $b = 3x$.

We also know that the perpendicular height $AD = 2.5$ meters, and the height forms a right-angled triangle with sides $l$, $b$, and $AD$.

Using the Pythagorean theorem in triangle $ACD$, we have: $l^2 = \left(\frac{b}{2}\right)^2 + AD^2$ Substitute the expressions for $l$, $b$, and $AD$: $(4x)^2 = \left(\frac{3x}{2}\right)^2 + (2.5)^2$ $16x^2 = \left(\frac{9x^2}{4}\right) + 6.25$ Multiply everything by 4 to eliminate the fraction: $64x^2 = 9x^2 + 25$ Simplify: $64x^2 - 9x^2 = 25$ $55x^2 = 25$ $x^2 = \frac{25}{55}$ $x^2 = \frac{5}{11}$ Take the square root: $x = \sqrt{\frac{5}{11}} \approx 0.6742 \text{ meters}$

Now, substitute back to find $l$ and $b$: $l = 4x = 4(0.6742) \approx 2.70 \text{ meters}$ $b = 3x = 3(0.6742) \approx 2.02 \text{ meters}$

Final Answer:

The length of the sides $l$ is approximately 2.70 meters.

Would you like further details or have any questions?

Here are 5 additional questions that build on this:

1. How can you calculate the area of triangle $ABC$ using the given dimensions?
2. What is the total surface area of the triangular prism if the depth of the prism is known?
3. How would you calculate the volume of this triangular prism?
4. How can we determine the angles within the triangle $ABC$?
5. Can the Pythagorean theorem be used if the triangle is not a right triangle?

Tip:

When dealing with geometric shapes, sketching the problem and labeling all known dimensions can make it much easier to visualize and solve.