Question

tell correct answer..... ​

Answer 1

Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Let the sides are

3x ,4x , 5x

Perimeter=900

$\qquad\quad {:}\longmapsto\sf Semi perimeter=s={\dfrac {900}{2}}=450$

According to Heron 's Formula

$\boxed{\sf s={\dfrac {a+b+c}{2}}}$

Substitute the values

$\qquad\quad {:}\longmapsto\sf {\dfrac {3x+4x+5x}{2}}=450$

$\qquad\quad {:}\longmapsto\sf {\dfrac {13x}{2}}=450$

$\qquad\quad {:}\longmapsto\sf 13x=900$

$\qquad\quad {:}\longmapsto\sf x={\dfrac {900}{13}}$

$\qquad\quad {:}\longmapsto\sf x=69.2$

$\qquad\quad {:}\longmapsto\sf x=69 (Approx)$

_____________________________

$\qquad\quad {:}\longmapsto\sf 3x=3×69=207$

$\qquad\quad {:}\longmapsto\sf 4x=4×69=276$

$\qquad\quad {:}\longmapsto\sf 5x=5×69=345$

____________________________

According to Heron 's Formula

$\boxed{\bf Area=\sqrt {s (s-a)(s-b)(s-c)}}$

Substitute the values

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {450 (450-207)(450-276)(450-345)}$

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {450×243×174×105}$

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {2,244,469,500}$

$\qquad\quad {:}\longmapsto\sf Area=47,375.8$

$\qquad\quad {:}\longmapsto\sf Area=47,375 units {}_{(Approx)}$

$\therefore{\underline{\boxed{\sf Area=47,375units.}}}$

Answer 2

Answer:

Let sides of the triangle are 3X , 5X and 4X.

Perimeter of triangle = 900 m

Sum of all three sides = 900 m

3X + 5X + 4X = 900

12X = 900

X = (900/12) m

X = 75 m

Therefore,

3X = 3 × 75 = 225 m

5X = 5 × 75 = 375 m

And,

4X = 4 × 75 = 300

Sides of the triangle are 225 m , 375 m and 300 m.

Let,

A = 225 m

B = 375 m

And,

C = 300 m

Semi perimeter ( S ) = 1/2 × ( A + B + C )

=> 1/2 × ( 225 + 375 + 300 )

=> 1/2 × ( 900 )

=> 450 m

( S - A ) = 450 - 225 = 225 m

( S - B ) = 450 - 375 = 75 m

And,

( S - C ) = 450 - 300 = 150 m

Therefore,

Area of triangle = ✓S ( S - A ) ( S - B ) ( S - C )

=> ✓450 × 225 × 75 × 150

=> ✓1139062500

=> 33750 m².

hope this helps you