Answer:
The sides of the equilateral triangle are 11.7 m.
Step-by-step explanation:
Let's find the area of the isosceles triangle:
[tex] A_{i} = \frac{bh}{2} [/tex]
Where:
b: is the base = 12 m
h: is the height
We can find the height by using Pitagoras:
[tex] x^{2} = \frac{b^{2}}{2} + h^{2} [/tex]
Where:
x is the hypotenuse = side of the triangle = 10 m
[tex] h = \sqrt{x^{2} - \frac{b^{2}}{2}} = \sqrt{(10)^{2} - 6^{2}} = 8 m [/tex]
Then, the area is:
[tex] A_{i} = \frac{12*8}{2} = 48 m^{2} [/tex]
Now, since the area of the isosceles triangle is equal to the area of the equilateral triangle:
[tex] A_{e} = A_{i} = 48 m^{2} [/tex]
[tex] A_{e} = \frac{bh}{2} [/tex]
The height of the equilateral triangle is given by:
[tex] b^{2} = \frac{b^{2}}{2} + h^{2} [/tex]
[tex] h = \sqrt{b^{2} - \frac{b^{2}}{2}} = \frac{b}{\sqrt{2}} [/tex]
Hence, the sides are:
[tex] A_{e} = \frac{1}{2}b\frac{b}{\sqrt{2}} = \frac{b^{2}}{2\sqrt{2}} [/tex]
[tex] b = \sqrt{A*2\sqrt{2}} = \sqrt{48*2\sqrt{2}} = 11.7 m [/tex]
Therefore, the sides of the equilateral triangle are 11.7 m.
I hope it helps you!
Answer:
The sides must be around 10.53 m
Step-by-step explanation:
You can calculate the area of isosceles dividing into 2 equal right triangles
Once you know that the area of the isosceles is 48 m²,solve for the side of the equilateral triangle
Formula for the Area: (A= area a = side)
A = (√3* a² ) / 4
48= (√3* a² ) / 4
Multiply both sides by 4
192 =√3* a²
Divide both sides by√3 ( √3 = 1.732050....)
110.851303 = a²
Square root on both sides
10 .5385...( 10.53 ) = a
