Question

the hypotenuse of a right angled triangle is 25 m if one side is 5 more than the other side find its area

Answer 1

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Answer 2

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

Assumption

Smaller side be p

Hence,

Other side be (p + 5)

${\boxed{\sf\:{Using\;Pythagoras\;Theorem}}}$

(H)² = (B) + (P)²

(25)² = (p)² + (p + 5)²

625 = p² + p² + 10p + 25

2p² + 10p - 625 + 25 = 0

2p² + 10p - 600 = 0

p² + 5p - 300 = 0

$\textbf{\underline{Splitting\;the\;Middle\;Term}}$

p² + 20p - 15p - 300 = 0

p(p + 20) - 15 (p + 20) = 0

(p - 15) (p + 20) = 0

p = 15, p = - 20

${\boxed{\sf\:{Negative\;Value\;will\;be\;Rejected}}}$

Hence,

p = 15 cm

Other side

= 15 + 5 = 20 cm

Therefore,

Area of triangle

$\tt{\rightarrow\dfrac{1}{2}\times b\times h}$

$\tt{\rightarrow\dfrac{1}{2}\times 15\times 20}$

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

= 150 cm²

Hence,

$\Large{\boxed{\sf\:{Area\;of\;Triangle=150cm^2}}}$