please find out the answer off 11and 12plz who will answer I will make it Brainliest answer .step by step answer correct it should be .
Answers
Question 11
Given in triangle ABC, XY is a horizontal line as : XY║BC
∠ABC = 90°
AB = 12cm
AY = 8cm
and
We know from side splitter theorem if a line is Parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
As we know,
So we can say that
then we get
YC = 16
So AC = 8 + 16 = 24cm
Now, apply Pythagoras theorem in triangle ABC
(ABC)² = (AB)² + (BC)²
⇒ ( 24)² = (12)² + (BC)²
⇒ (BC)² = 576 - 144
⇒ (BC)² = 432
⇒ BC =
⇒ BC = 2078 cm
So,
AC = 24 cm and BC = 20.78 cm
Question 12
For right angled triangle,
By Pythagoras theorem,
ab² + bc² = ac²
12 (i)
(x-3)² + (x+4)² = (x+6)²
⇒ x² - 6x + 9 + x² + 8x + 16 = x² + 12x + 36
⇒ 2x² +2x + 25 = x² + 12x + 36
⇒ x² -10x -11 = 0
x = (-b ± √(b² - 4ac))/2a
⇒ x = {-(-10) ± √(100+44)}/2
⇒ x = (10 ± √144)/2
⇒ x = (10 ± 12)/2
x = (10 + 12)/2 OR x = (10 - 12)/2
x = 22/2 OR x = -2/2
x = 11 OR x = -1
Since side cannot be negative
So,
x = 11
Therefore sides of triangle are
x-3 = 11-3 = 8
x+4 = 11+4 = 15
x+6 = 11+6 = 17