Answer:
Step-by-step explanation:
1) the triangle on the right is half of an equilateral one, so the minor leg is 9
the left one has the two legs congruent
so we have
2x^2 = 81
x^2 = 81/2
x = 9/√2 = 9/2 √2 (at the numerator)
2) the top triangle has the congruents leg
hypotenuse^2 = 2(6√6)^2
hypotenuse^2 = 2(216)
hypotneuse^2 = 432
hypotenuse = √2^4 * 3^2 * 3
hypotenuse = 12√3
the triangle in the bottom is half of the an equilateral one, so
x = 12√3 * 2 = 24√3
3) the left triangle has congruent legs
7^2 = leg^2 + leg^2
49 = 2leg^2
leg^2 = 49/2
leg = 7/√2 = (7√2)/2
the right triangle is half of an equilateral one
x = 7√2/2 * √3 = 7/2 √6 (at the numerator)
4) the rifht triangle has two congruent legs
hy^2= 2(7√6)^2
hy^2 = 2(294)
hy^2 = 588
hy = √2^2 * 7^2* 3
hy = 14√3
the triangle on the left is half of an equilteral one: so
x = 14