A pentagon is formed by putting together three identical equilateral triangles and one larger equilateral triangle with length of edge equal to 2 times that of the smaller equilateral triangle. If the perimeter of the smaller triangle is 42 cm, what is the perimeter of the pentagon?
i need help setting up an equation for this problem
let each side of the smaller triangles be x
then the length of the larger triangle is 2x
place 2 of the smaller triangles along a side of the larger, the third of the smaller fits between the two other small ones.
"If the perimeter of the smaller triangle is 42 cm" -----> 3x=42 so
x=14
now "walk" around the perimeter of the pentagon, I see x+x+x+2x+2x
do you follow that?
The two figures are similar find the ratios (A toB) of the perimeter
Yes, I understand. So let's break it down step by step.
First, you define the length of each side of the smaller equilateral triangle as x. Since the perimeter of the smaller triangle is 42 cm, we can set up the equation as 3x = 42. This is because an equilateral triangle has three equal sides.
Next, you determine the length of the larger equilateral triangle. You mention that the length of the larger triangle is 2x, as it is twice the length of the smaller triangle.
Then, you place two of the smaller triangles along a side of the larger triangle, and the third smaller triangle fits between the two other small ones.
Now, let's calculate the perimeter of the pentagon. We "walk" around the perimeter and observe that it consists of the sum of the sides of the three smaller triangles (x + x + x) and the sum of the sides of the two larger triangles (2x + 2x).
Putting it all together, the perimeter of the pentagon is x + x + x + 2x + 2x.
Simplifying, we have 3x + 4x, which equals 7x.
Therefore, the perimeter of the pentagon can be expressed as 7x. To find the actual perimeter, substitute x with its value of 14 (as we found earlier, x = 14).
Hence, the perimeter of the pentagon is 7 * 14 = 98 cm.