Question

Traffic rules play a very important role in the traffic system of a country. These rules are made for

avoiding traffic jams and accidents in cities and towns. In this order, a side wall of Dwarka Das Park

painted in black colour with a message, ‘TO FOLLOW THE TRAFFIC RULES’. If the sides of wall are 15m,

11m and 6m respectively. Then solve the following question:-

(i) Find the semi perimeter of Triangle.

(a) 12m (b) 13m (c) 14m (d) 16m

(ii) Find the area( in m2

) of wall.

20√2 (b) 18√3 (c) 30√2 (d) 32√3

(iii) Write the formula to find the semi perimeters of triangle.

(a) S=−−

2

(b) =

++

3

(c ) =

++

2

(d)S= √ + +

(Iv) Which mathematical concept is used to solve the above problem?

(a) Area of parallelogram (b) Heron’s formula (c) Surface area and volumes (d) None of these

(iv) If the side of an equilateral triangle is P, then area of triangle is

(a) √3

4

P

2

(b) √3 P

2 (c) √3

2

P

2 (d) √3

4

P​

Answer 1

Step-by-step explanation:

26. d 16m

27. d 32.49

28. c s=a+b+c /2

29. Herons formula

30. √3/4a²

Answer 2

Answer:(1)Semi perimeter of the triangle is $16m$.

(2)Area of triangle is $20\sqrt{2} m^{2}$.

(3)The semi perimeters of triangle the formula is given by,

⇒                                           $s=\frac{a + b + c}{2}$

where $a,b$ $and$ $c$ are the sides of the given triangle.

(4)To solve the given problem the concept used is Heron's formula which is used for calculating the area of given triangle.

(5)Area of equilateral triangle whose side is P is  $\frac{\sqrt{3} }{4} P^{2}$.

Step-by-step explanation:

Given:Traffic rules play a very important role in the traffic system of a country. These rules are made for avoiding traffic jams and accidents in cities and towns. In this order, a side wall of$Dwarka$ $Das$ Park painted in black $colour$ with a message, ‘TO FOLLOW THE TRAFFIC RULES’. If the sides of wall are 15 m, 11 m and 6m respectively.

To find:(i) Find the semi perimeter of Triangle.

(a) 12 m (b) 13 m (c) 14 m (d) 16 m

(ii) Find the area( in $m^{2}$) of wall.

(a)20√2 (b) 18√3 (c) 30√2 (d) 32√3

(iii) Write the formula to find the semi perimeters of triangle.

(a) S =−2

(b) s=+3

(c ) =+2

(d)S= √ 2

(Iv) Which mathematical concept is used to solve the above problem?

(a) Area of parallelogram (b) Heron’s formula (c) Surface area and volumes (d) None of these

(v) If the side of an equilateral triangle is P, then area of triangle is

(a)$\frac{\sqrt{3} }{4} P^{2}$

(b) $\sqrt{3} P^{2}$

(c) $\frac{\sqrt{3} }{P^{2} }$

(d) $\frac{\sqrt{3} }{4} P$

Explanation:

Step 1: As sides of the triangle is 15 m,11 m and 6 m respectively.

∵          Semi perimeter of the triangle $=\frac{a + b + c}{2}$

           where $a = 15m,b = 11m$ and $c = 6m$

∴ Semi perimeter of the triangle $=\frac{15 + 11 + 6}{2}$

                                                      $= \frac{32}{2}$

                                                      $= 16m$

∴ Semi perimeter of the triangle is $16m$.

Step 2: As sides of triangle are 15 m,11 m and 6 m respectively.

We have already determined the semi perimeter of the triangle in previous step.

∴ Semi perimeter of the triangle $s$ $=\frac{a + b + c}{2}$ $=\frac{15 + 11 + 6}{2}$ $=$ $16m$.

Now to find area of triangle we use Heron's formula which given by,

⇒                 Area of triangle $= \sqrt{s(s-a)(s-b)(s-c)}$

                                              $= \sqrt{16(16-15)(16-11)(16-6)}$

                                              $= \sqrt{16(1)(5)(10)}$

                                              $= \sqrt{800}$

                                              $= 20\sqrt{2} m^{2}$

∴                 Area of triangle is $20\sqrt{2} m^{2}$.

Step 3:To find the semi perimeters of triangle the formula is given by,

⇒                                           $s=\frac{a + b + c}{2}$

                  where $a,b$ $and$ $c$ are the sides of the given triangle.

Step 4: To solve the given problem the concept used is Heron's formula which is used for calculating the area of given triangle.

Step 5:If sides of the equilateral triangle is P

So,       Semi perimeter of the triangle $=\frac{P + P + P}{2}$

                                                              $= \frac{3P}{2}$

∴Area of equilateral triangle $= \sqrt{s(s-P)(s-P)(s-P)}$

                                               $= \sqrt{\frac{3P}{2} (\frac{3P}{2}-P)(\frac{3P}{2}-P)(\frac{3P}{2}-P) }$

                                               $= \sqrt{\frac{3P}{2}(\frac{P}{2} )(\frac{P}{2} )(\frac{P}{2} ) }$

                                               $= \sqrt{\frac{3}{16}P^{4} }$

                                               $= \frac{\sqrt{3} }{4} P^{2}$

∴   Area of equilateral triangle whose side is P is  $\frac{\sqrt{3} }{4} P^{2}$.

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