Question

Length of wire is 20 cm long. It is bent at right angles to form the two A straight shorter sides of a right angled triangle. If the triangle's area is 30 cm find the length of the hypotenuse and the triangle's perimeter

Answer 1

Kawat membentuk sisi alas dan tinggi segitiga siku-siku.
misalkan:
alas = a
tinggi = t
Dengan demikian:
a + t = 20 cm
a = 20 - t

L = 1/2 a t
30 = 1/2 . (20 - t).t
60 = 20t - t²
t² - 20t + 60 = 0

t = (20 +/- √[ (-20)² - 4.1.60) ]/2.1
  = (20 +/- √(400 - 240) ]/2
  = (20 +/- √160)/2
  = (20 +/- 4√10)/2
  = 10 +/- 2√10

t = (10 + 2√10) cm
a = 20 - (10 + 2√10)
   = (10 - 2√10) cm

manentukan sisi miring (r) kita gunakan dalil phytagoras

r² = a² + t²
   = (10 - 2√10)² + (10 + 2√10)²
   = 100 - 40√2 + 40 + 100 + 40√2 + 40
   = 280
r = √280
  = 2√70 cm

Keliling segitga:

K = a + t + r
   = 10 - 2√10 + 10 + 2√10 + 2√70
   = (20 + 2√70)  cm