14. The sides of a triangular plot of land are $3\frac{1}{4}$ metres, $2\frac{1}{4}$ metres, and $3\frac{1}{2}$ metres. Find the perimeter of the plot.

Question

High School

We appreciate your visit to 14 The sides of a triangular plot of land are 3 frac 1 4 metres 2 frac 1 4 metres and 3 frac 1 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

danjohnbrain danjohnbrain · Answer 1 · 2024-09-20T06:06:23-04:00

To find the perimeter of a triangular plot of land, we need to add up the lengths of all its sides.

Let's break down the given side lengths:

The first side is given as [tex]3\frac{1}{4}[/tex] meters. As a mixed number, this is equal to [tex]3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}[/tex] meters.
The second side is [tex]2\frac{1}{4}[/tex] meters. As a mixed number, this becomes [tex]2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}[/tex] meters.
The third side is [tex]3\frac{1}{2}[/tex] meters. As a mixed number, this is [tex]3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}[/tex] meters.

To add these fractions together, we first need a common denominator. The least common multiple of 4 and 2 is 4. Thus:

[tex]\frac{13}{4}[/tex] remains the same.
[tex]\frac{9}{4}[/tex] remains the same.
[tex]\frac{7}{2}[/tex] can be converted to a denominator of 4 as [tex]\frac{7 \times 2}{2 \times 2} = \frac{14}{4}[/tex].

Now, we add them all together:

[tex]\text{Perimeter} = \frac{13}{4} + \frac{9}{4} + \frac{14}{4} = \frac{13 + 9 + 14}{4} = \frac{36}{4} = 9[/tex]

Therefore, the perimeter of the triangular plot of land is 9 meters.