Question

Refer to the attachment please!
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Answer 1

Answer:

We have to show that

((3√2-2√3)/(3√2+2√3)) + (2√3/(√3-√2)) = 11

L.H.S = ((3√2-2√3)/(3√2+2√3)) + (2-√3/ (√3-√2))

By rationalization we get

=((3-√2-2√3)/(3√2+2√3))((3√2-2√3)/

(3√2-2√3)) + (2√3/(√3-√2))((√3+√2)/ (√3+√2))

= (3-√2-2√3)² / (9(2) - 4(3))+ ((2√3) (√3+√2))/(3-2)

= (( 18 + 12 - 12√6) / (18 - 12)) + ( 2(3) + 2√6)/1

= (( 30-12-√6)/6) + 6+2√6

= 5-2√6 + 6 + 2√6

= 11

= R.H.S

Hence

L.H.S R.H.S

Answer 2

Answer:

Plate

Step-by-step explanation:

is answer

Step-by-step explanation:

We are given that two sides of triangular field are 85 M and 154 m

Perimeter of triangle = 324 M

Let the third side be x

Perimeter of triangle =Sum of all sides

$\Rightarrow85+154+x </p><p>$

$\Rightarrow239+x$

Since we are given that Perimeter of triangle = 324M;

$So, \Rightarrow 324 = 239 +x;</p><p>$

$\Rightarrow324 - 239 = x; \\ </p><p> </p><p> \Rightarrow8 5 = x \\ </p><p>$

Now we will use heron's formula to find the area of triangle

$\rightarrow \: a = 85m \\ </p><p> \rightarrow \: b = 154m; \\ </p><p> \rightarrow \: c = 85m; \\ </p><p> </p><p>Area = \sqrt{(s(s - a) \times (s - b) \times (s - c))} ; \\ \\ s \rightarrow\frac{ (a + b + c)}{2}$

Substitute the values:

$\rightarrow \: s = \frac{(85 + 154 + 85)}{2} \\ \\ \\ \\ </p><p></p><p></p><p>\Rightarrow s = 162; \\ \\ \\ \\ </p><p> </p><p>\Rightarrow \: Area =; \sqrt{162(162-85)(162-154)(162-85)} ;</p><p>$

${\boxed{ \green {\Rightarrow \: Area = 2772}}}$

So, Area of triangle is 2772

Now rto find the length of the perpendicular from the opposite vertex on the site measuring 154 m

$Area = \frac{1}{2} \times B a s e \times H e i g h t;$

2772 = 1/2 ×154 ×H e i g h t;

(2772 ×2)/154 = Height;

36 = Height

Hence Area of triangle is 2772 and he length of the perpendicular from the opposite vertex on the site measuring 154 m is 36 m