you use Pythagoras theorem. Square of the Hypotenuse = square of the other 2 sides i.e ac squared = ab squared + bc square = 22 Squared + 32 Squared = 484 + 1024 = 1508 so ac = square root of 1508 = 38.83 cm(2 d.p)
36/√3
It would be a straight line of length bc
12 cm
AB + AC + BC = 48 AB + (AB +9) + (AB + 9 + 3) = 48 Solve and AB = 9 So AB = 9, AC = 18 and BC = 21
If the quadrilateral is a square then all of its sides are the same length. ac is not one of the sides but is a diagonal which forms the hypotenuse of a right angle triangle with sides ab and bc. According to Pythagoras the sum of the square of the hypotenuse is equal to the sum of the squares of the other two sides. As side ab measures 10 then 10 squared = 100. Side bc has the same measurements. The square of side ac must equal 200 (100 + 100) so the length of side ac must equal the square root of 200 (100 + 100) which is 14.14 (to 2 decimal places).
\8
If 2 segments have the same length they are known as 'congruent segments' IE: segment AB=segment AC (or AB=AC) then AB @ AC (or AB is congruent to AC)
you use Pythagoras theorem. Square of the Hypotenuse = square of the other 2 sides i.e ac squared = ab squared + bc square = 22 Squared + 32 Squared = 484 + 1024 = 1508 so ac = square root of 1508 = 38.83 cm(2 d.p)
To find the length of AC, use the Pythagorean theorem. AC equals the square root of (AB squared + BC squared), which is the square root of (9 squared + 12 squared), giving AC = square root of (81 + 144) = square root of 225 = 15 centimeters.
never
sqrt(ab^2 + bc^2)
Assuming that AB and AC are straight lines, the answer depends on the angle between AB and AC. Depending on that, BC can have any value in the range (22, 46).
You cannot prove it since it is not true for a general quadrilateral.
36/√3
16cm
The length is sqrt(61) units.