Math, asked by 20180131, 9 months ago

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 .​

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Answered by Unni007
2

Question 11

Given in triangle ABC, XY is a horizontal line as : XY║BC

∠ABC = 90°

AB = 12cm

AY = 8cm

and

\frac{AX}{XB} =  \frac{1}{2}

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, \frac{AX}{XB}  =  \frac{1}{2}

So we can say that \frac{AY}{YC}  =  \frac{1}{2}

then we get \frac{8}{YC} =  \frac{1}{2}

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 = \sqrt{432

⇒ 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

Therefore the sides are 8 cm , 15 cm , 17 cm

12(ii)

Substitute the values as same as the above question.

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