Question

The perimeter of a triangular window is 141 inches. The ratio of the side lengths of the window is$11:18:18$. Draw and label a diagram of the window. What are the side lengths of the window? Classify the window by its side lengths.

Short answer

The length of the sides of the window measures 33 inches, 54 inches and 54 inches respectively and the window is of the shape of an isosceles triangle.

Step-by-step solution

Step 1. Given Information.

Ratio of the side length measures in a triangle is given as$11:18:18$.

Perimeter of the triangular window is given as 141 inches.

Step 2. Calculation.

Let the side measures be 11x, 18x, and 18x.

The perimeter of the window is given as 141 inches. Hence,

$11x+18x+18x=141$

Add all the x together,

$47x=141$

Divide both the sides by 47.

$\frac{47x}{47}=\frac{141}{47}$

This will give the value of$x=3$.

Hence the side measures are:

First side is 11x so, multiply 11 with 3.

$\begin{array}{l}x=11\times 3\\ =33\end{array}$

Second side and third side are same as 18x, so multiply 18 with 3.

$\begin{array}{l}x=18\times 3\\ =54\end{array}$

The window is an isosceles triangle as shown below.

Step 3. Conclusion.

The side of the length measures of the triangle are 33 inches, 54 inches and 54 inches respectively.

As can be seen two sides of the triangle is same and one is different, the shape of the window is of an isosceles triangle.