Question

The longest side of right angled triangle is 125cm and the remaining two sides is 100cm. Find its area using heron's formula.

Answer 1

herons formula is s=a+b+c/2
125+100+100+/2=162.5
s=162.5
area=square root of s(S-a)(s-b)(s-c)

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\textbf{\underline{Largest\;side\;of\;Triangle}}$

= 125 m

$\textbf{\underline{One\;side}}$

= 100 m

$\textbf{\underline{Contradiction}}$

Perpendicular = 100 m

$\textbf{\underline{Using\;Pythagoras\;Theorem}}$

(H)² = (B)² + (P)²

(125)² = (B)² + (100)²

15625 = (B)² + 10000

(B)² = 15625 - 10000

(B)² = 5625

B = √5625

$\textbf{\underline{Base\;of\;third\;side}}$

= 75 m

$\textbf{\underline{Semi\;Perimeter}}$

$\tt{\rightarrow\dfrac{a+b+c}{2}}$

$\tt{\rightarrow\dfrac{125+100+75}{2}}$

$\tt{\rightarrow\dfrac{300}{2}}$

s = 150 m

$\textbf{\underline{Using\;Herons\;Formula}}$

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow\sqrt{150\times(150-125)(150-100)(150-75)}}$

$\tt{\rightarrow\sqrt{150\times 25\times 50\times 75}}$

$\tt{\rightarrow\sqrt{14062500}}$

= 3750 m²

$\Large{\boxed{\sf\:{Area\;of\;Triangle=3750\;m^2}}}$