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Find the perimeter of the polygon if

5 cm

6 cm

7 cm

P = ? Cm

Find the perimeter of the polygon if 5 cm 6 cm 7 cm P = ? Cm-example-1
User Thikonom
by
9.1k points

2 Answers

5 votes

Answer:

(2) is the answer for your question

User Michasaucer
by
8.8k points
3 votes

The perimeter of the polygon is 143/6 cm or approximately 23.83 cm.

To find the length of AD, we can use the fact that opposite angles in a parallelogram are equal. Since ∠B ≅ ∠D, we can conclude that △ABD is similar to △CDB (by Angle-Angle similarity).

Let x represent the length of AD.

Using the properties of similar triangles:

AD/AB = DC/BC

So, x/5 = 7/6

Cross-multiplying, we get:

6x = 5 * 7

6x = 35

x = 35/6 cm

Now that we have found the length of AD, we can calculate the perimeter of the polygon by adding up all the sides:

Perimeter = AB + BC + CD + AD

Perimeter = 5 cm + 6 cm + 7 cm + 35/6 cm

Perimeter = 18 cm + 35/6 cm

Perimeter = 108/6 cm + 35/6 cm

Perimeter = (108 + 35) / 6 cm

Perimeter = 143/6 cm

So, the perimeter of the polygon is 143/6 cm or approximately 23.83 cm.

User Taylor Bird
by
8.0k points

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