Question

The slide in a park is in a park is in the shape as given below. One triangular side of the construction is
painted with a message "KEEP THE PARK CLEAN AND GREEN". The sides of the triangle are 11m, 15m, and
6m.

i) The semi perimeter of the triangle is a) 30m b) 16m c) 32m d) 15m
ii) The formula to find the perimeter of the triangle is a) (a+b+c) b) a+b+c c) 3a d) 2(a+b+c)
2
iii) The area of the triangle is a) 15m2
b) 30 m2
c) 20√2 m2
d) 20√3 m2
iv) The perimeter of the triangle is a) 16m b) 32m c) 30 m d)

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

• The slide in a park is in the shape of triangle.

• One triangular side of the construction is painted with a message "KEEP THE PARK CLEAN AND GREEN".

• The sides are 11m, 15m, and 6m.

Let assume that

• a = 11 m

• b = 15 m

• c = 6 m

We know,

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So,

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct.

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$\large\underline{\sf{Solution-}}$

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$\large\underline{\sf{Solution-}}$We know, Perimeter of a triangle is defined as sum of all the sides of a triangle.

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$\large\underline{\sf{Solution-}}$We know, Perimeter of a triangle is defined as sum of all the sides of a triangle. Here, sides are represented as a, b, c

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$\large\underline{\sf{Solution-}}$We know, Perimeter of a triangle is defined as sum of all the sides of a triangle. Here, sides are represented as a, b, cSo,

We know, $\underline{\boxed{\sf Semi Perimeter \ of \ a \ triangle, \: s=\dfrac{1}{2} (a+b+c)}}$So, $\rm :\longmapsto\:s = \dfrac{11 + 15 + 6}{2}$$\rm :\longmapsto\:s = \dfrac{32}{2}$$\rm \implies\:\boxed{\tt{ s \: = \: 16 \: m}}$So, option (b) is correct. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$\large\underline{\sf{Solution-}}$We know, Perimeter of a triangle is defined as sum of all the sides of a triangle. Here, sides are represented as a, b, cSo, Perimeter of triangle = a + b + c

So, option (b) is correct.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\sf{Solution-}}$

We have

• a = 11 m

• b = 16 m

• c = 5 m

• s = 16 m

We know,

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

So,

$\rm :\longmapsto\:Area = \sqrt{16(16 - 11)(16 - 15)(16 - 6)}$

$\rm :\longmapsto\:Area = \sqrt{16 \times 5 \times 1 \times 10}$

$\rm :\longmapsto\:Area = \sqrt{4 \times 4 \times 5 \times 1 \times 2 \times 5}$

$\rm :\longmapsto\:Area = 4 \times 5 \times \sqrt{2}$

$\bf\implies \:Area = 20 \sqrt{2} \: {m}^{2}$

So, option (c) is correct.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\sf{Solution-}}$

Perimeter of triangle = a + b + c = 11 + 15 + 6 = 32 m

So, option (b) is correct.