Answer:
see explanation
Explanation:
(a)
perimeter (P) is calculated as
P = 2(l + b) ← l is the length and b the breadth
given l = x and P = 20 , then
2(x + b) = 20 ( divide both sides by 2 )
x + b = 10 ( subtract x from both sides )
b = 10 - x
Using Pythagoras' identity in the right triangle
x² + (10 - x)² = 8²
x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )
2x² - 20x + 36 = 0 ( divide through by 2 )
x² - 10x + 18 = 0 ← as required
(b)
solve using the method of completing the square
x² - 10x + 18 = 0 ( subtract 18 from both sides )
x² - 10x = - 18
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 18 + 25
(x - 5)² = 7 ( take square root of both sides )
x - 5 = ±
( add 5 to both sides )
x = 5 ±
Then
x = 5 -
≈ 2.35 ( to 3 significant figures )
x = 5 +
≈ 7.65 ( to 3 significant figures )