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# help #2

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5 tysm

Jun 29, 2021

#1
+3

Area of equilateral triangle: $$\frac{\sqrt{3}}{4}s^2$$

Area of regular hexagon: $$\frac{3\sqrt{3}}{2}s^2$$

If the perimeter of the triangle is 18, then one side is 6, therefore the area of it is,

$$\frac{\sqrt{3}}{4}\cdot36$$

$$area = 9\sqrt{3}$$

Because their areas are equal,

$$\frac{3\sqrt{3}}{2}s^2 = 9\sqrt{3}$$

Simplify,

$$3\sqrt{3}\cdot s^2 = 18\sqrt{3}$$

$$s^2 = 6$$

$$s = \sqrt{6}$$

There are 6 sides in a hexagon, so the perimeter is, $$\sqrt{6} \cdot 6 = 6\sqrt{6}$$. 6 + 6 = 12, so that's the answer.

EDIT: I messed up my arithmetic

Jun 29, 2021
edited by Awesomeguy  Jun 29, 2021

#1
+3

Area of equilateral triangle: $$\frac{\sqrt{3}}{4}s^2$$

Area of regular hexagon: $$\frac{3\sqrt{3}}{2}s^2$$

If the perimeter of the triangle is 18, then one side is 6, therefore the area of it is,

$$\frac{\sqrt{3}}{4}\cdot36$$

$$area = 9\sqrt{3}$$

Because their areas are equal,

$$\frac{3\sqrt{3}}{2}s^2 = 9\sqrt{3}$$

Simplify,

$$3\sqrt{3}\cdot s^2 = 18\sqrt{3}$$

$$s^2 = 6$$

$$s = \sqrt{6}$$

There are 6 sides in a hexagon, so the perimeter is, $$\sqrt{6} \cdot 6 = 6\sqrt{6}$$. 6 + 6 = 12, so that's the answer.

EDIT: I messed up my arithmetic

Awesomeguy Jun 29, 2021
edited by Awesomeguy  Jun 29, 2021
#2
+1

Nice solution Awesomeguy   !!!!   CPhill  Jun 29, 2021
#3
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CPhill, I don't think thats correct tho, the ans is 12.

justinwh333  Jun 29, 2021
#4
0

Yeah sorry i messed up my math

Awesomeguy  Jun 29, 2021
#5
+1

No biggie....just a math mistake.....you  had  the correct approach   !!!!   CPhill  Jun 29, 2021