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Question

1. A diagonal of a square has length 8. What is the perimeter of the square? 

2. Find the altitude of an equilateral triangle if each side is 10 units long 

Answer 1

diagonal of a square = 8

sides = 8/sq2 = 4sqr2 = about 4(1.414) = 5.656

perimeter = 4 x a side = 16sqr2 = about 4(5.656) = 22.624

use the Pythagorean Theorem

hypotenuse (the diagonal) squared = sum of squares

8^2 = (4sqr2)^2 + (4sqr2)^2 = 16(2) + 16(2)

64 = 32(2) = 64

side of an equilateral triangle = 10

construct a right triangle with hypotenuse = 10, base = 5, altitude squared = 10^2 - 5^2 - 100-25 = 75

altitude = sqr75 = 5sqr3