Answer:
ii) c = 4 iii) c = 8
Step-by-step explanation:
A = x axis intercept = 1/2 c
B = y axis intercept = c
ii) Area of a triangle = 1/2 x base x height
4 = 1/2 x (1/2)c x c
c² = 16
c = 4
iii) 2√5 will be the hypotenuse of a right-angled triangle with base 1/4 c and height 1/2 c
(2√5)² = (1/4 c)² + (1/2 c)²
20 = 1/16 c² + 1/4 c²
20 = 5/16 c²
c² = 64
c = 8
Answer:
x = 112°
Step-by-step explanation:
To find the value of x, you need to understand the properties of vertical and supplementary angles and know that the sum of angles inside a triangle is 180°.
F + s = 10
| f - s | = 18
-------
This means that:
f = 10 - s
And also that:
| f - s | = 18
(f-s)²=18²
f²- 2sf + s² = 324
But f=10-s
So...
(10-s)² - 2s(10-s) + s² = 324
(10-s)(10-s) - 20s + 2s² + s² = 324
100 - 20s + s² - 20s + 2s² + s² = 324
4s² - 40s + 100 = 324
4s² - 40s + 100 - 324 = 0
4s² - 40s - 224 = 0
1/4 * (4s² - 40s - 224) = 1/4 * 0
s² - 10s - 56 = 0
(s-14)(s+4)=0
So s can be either 14 or -4.
When s = 14, f = -4.
When s = -4, f = 14.
