Question

16
" What is the area of an isosceles triangle whose base is 30 cm and lenght of two congruent
sides is 17 cm ?
​

Answer 1

AnswEr :

$\bf{Given}\begin{cases}\sf{Base = 30 cm}\\\sf{Equal \:Sides \:of \: Isosceles \: \triangle= 17 cm}\\ \sf{Find \:the \:Area \:of \:Triangle}\end{cases}$

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{2cm}\begin{picture}(16,4)\put(8.8,3){\large{A}}\put(7.8,1){\large{B}}\put(10.1,1){\large{C}}\put(8,1){\line(1,0){2}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.6,1.9){\mathsf{\large{17 cm}}}\put(7.9,1.9){\mathsf{\large{17 cm}}}\put(8.8,0.8){\matsf{\large{30 cm}}}\end{picture}$

• First we will find the Semi Perimeter :

$\begin{lgathered}\longrightarrow \tt Semi \:Perimeter = \dfrac{Sum \:of \:Sides}{2} \\ \\\longrightarrow \tt s = \dfrac{a + b + c}{2} \\ \\\longrightarrow \tt s = \dfrac{30 + 17 + 17}{2}\\ \\\longrightarrow \tt s = \cancel\dfrac{64}{2} \\ \\\longrightarrow \blue{\tt s = 32}\end{lgathered}$

$\rule{300}{1}$

• Calculation of Area of Triangle :

$\begin{lgathered}\longrightarrow \tt Area_{\tiny \triangle ABC}= \sqrt{s(s - a)(s - b)(s - c)} \\ \\\longrightarrow \tt Area_{\tiny \triangle ABC}= \sqrt{32(32 - 30)(32 - 17)(32- 17)} \\ \\\longrightarrow \tt Area_{\tiny \triangle ABC}= \sqrt{32 \times 2\times15 \times15}\\ \\\longrightarrow \tt Area_{\tiny \triangle ABC}= \sqrt{64 \times 15 \times 15} \\ \\\longrightarrow \tt Area_{\tiny \triangle ABC}= \sqrt{(8 \times 8) \times (15 \times 15)} \\ \\\longrightarrow \tt Area_{\tiny \triangle ABC}= 8 \times 15 \\ \\\longrightarrow \boxed{\orange{\tt Area_{\tiny \triangle ABC}= 120 \:{cm}^{2}}}\end{lgathered}$

⠀

∴ Area of Triangle will be 120 cm².

#answerwithquality #BAL

Answer 2

Answer:

$\bold\red{Area=120{cm}^{2}}$

$\huge\underline\mathfrak{\sf{Solution:}}$

• Base of isosceles triangle(b) = 30 cm

• Congruent sides(a) = 17 cm

• Area of the triangle =?

Area of isosceles triangle:-

$\longrightarrow\tt \frac{b}{4} \sqrt{4{a}^{2}-{b}^{2}}$

$\longrightarrow\tt \frac{30}{4}\sqrt{4\times{17}^{2}-{30}^{2}}$

$\longrightarrow\tt 7.5 \sqrt{1156-900}$

$\longrightarrow\tt 7.5\times\sqrt{256}$

$\longrightarrow\tt 7.5\times 16$

$\longrightarrow\tt 120 {cm}^{2}$

Hope it helps you ♥ ♥ ♥