Math

QuestionFind the perimeter of a figure made of two congruent equilateral triangles, given that AD=DC=xAD = DC = x.

Studdy Solution

STEP 1

Assumptions1. The figure is composed of two congruent equilateral triangles. . The lengths of AD and DC are equal.
3. The length of AD is represented by x.

STEP 2

In an equilateral triangle, all sides are equal. Therefore, if AD = x, then the other sides of the triangle (AB and BD) are also equal to x.

STEP 3

Since the figure is composed of two congruent equilateral triangles, the sides of the second triangle (BC, CD, and DB) are also equal to x.

STEP 4

The perimeter of a figure is the sum of the lengths of all its sides. Therefore, to find the perimeter of the figure, we need to add up all the sides.
Perimeter=AB+BD+DC+CB+BAPerimeter = AB + BD + DC + CB + BA

STEP 5

Substitute the values of the sides with x.
Perimeter=x+x+x+x+xPerimeter = x + x + x + x + x

STEP 6

Calculate the perimeter of the figure in terms of x.
Perimeter=5xPerimeter =5xTherefore, the perimeter of the figure in terms of x is5x.

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