Question

the side of triangle 18cm24cmand30cmfind the areafind the area of the triangle and hens find the hight corresponding to the side measuring 24 cm​

Answer 1

Step-by-step explanation:

S of ∆ = a+b+c/2

= 18+24+30/2

= 72/2

= 36 cm

Area of ∆ = √S(S-a)(S-b)(S-c)

= √36(36-18)(36-24)(36-30)

= √36 × 18 × 12 × 6

= √46656

= 216 cm2

Area of ∆ = 1/2 × b × h

=> 216 cm2 = 1/2 × 24 × h

=> 216 cm2 = 12h

Therefore, h = 216/12

= 18 cm

Hope it helps :)

Answer 2

AnswEr :

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(6,8)\linethickness{0.075mm}\put(1, .5){\line(2, 1){3}}\put(4, 2){\line(-2, 1){2}}\put(2, 3){\line(-2, -5){1}}\put(.7, .3){ A }\put(4.05, 1.9){ B }\put(1.7, 2.95){ C }\put(3.2, 2.5){ 18 cm }\put(0.6,1.7){ 24 cm }\put(2.7, 1.05){ 30 cm }\end{picture}$

$\rule{100}{2}$

• First we will find the Semi Perimeter :

$\longrightarrow \sf Semi \:Perimeter = \dfrac{Sum \:of \:Sides}{2} \\\\\\\longrightarrow \sf s = \dfrac{a + b + c}{2} \\\\\\\longrightarrow \sf s = \dfrac{18 + 24 + 30}{2}\\\\\\\longrightarrow \sf s = \cancel\dfrac{72}{2} \\\\\\\longrightarrow \blue{\sf s = 36}$

$\rule{220}{1}$

• Calculation of Area of Triangle :

$\longrightarrow \sf Area_{\tiny \triangle ABC}= \sqrt{s(s - a)(s - b)(s - c)} \\\\\\\longrightarrow \sf Area_{\tiny \triangle ABC}= \sqrt{36(36 - 18)(36 - 24)(36-30)} \\\\\\\longrightarrow \sf Area_{\tiny \triangle ABC}= \sqrt{36 \times18 \times12\times6}\\\\\\\longrightarrow \sf Area_{\tiny \triangle ABC}= \sqrt{(6 \times6) \times(6\times3) \times(3 \times 2 \times2) \times6} \\\\\\\longrightarrow \sf Area_{\tiny \triangle ABC}= \sqrt{(6 \times 6)(6 \times 6)(3 \times 3)(2 \times2)} \\\\\\\longrightarrow \sf Area_{\tiny \triangle ABC}= 6\times6\times 3 \times 2 \\\\\\\longrightarrow \boxed{\sf Area_{\tiny \triangle ABC}= 216\:{cm}^{2}}$

⠀

∴ Hence, Area of Triangle will be 216 cm².

$\rule{220}{2}$

• Base = 24 cm
• Area of Triangle = 216 cm²
• Height = ?

$\implies\tt Area = \dfrac{1}{2} \times b \times h\\\\\\\implies\tt 216 = \dfrac{1}{2} \times24 \times h\\\\\\ \implies \tt \cancel\dfrac{216 \times 2}{24} = h\\\\\\\implies\red{\boxed{\tt h = 18 \:cm}}$

⠀

∴ Height to the base 24 cm will be 18 cm.