Question

The perimeter of a right angled triangle measures 234 m and the hypotenuse measures 97 m. Then, the other two sides of the triangle are measured as?​

Answer 1

Answer:

⭐Question:-

The perimeter of a right angled triangle measures 234 m and the hypotenuse measures 97 m. Then, the other two sides of the triangle are measured as?

⭐Answer:-

Solution:-

$Let \: a , \: b \: and \: c m. \: are \: the \: sides \: of \: a \: right \: angled \: triangle \: ABC \: in \: which \\ hypotenuse \: is \: c , \: acordingly:-\\ a+b+c = 234…………………..(1). \: and c= \\ 97 m. , putting \: c \: = \: 97 \: in \: eqn. \: (1) \\ a+b+97=234. \\ or. a+b = 137…………………(2). , \: \\ In right \: angled \: triangle \: ABC , \: a^2+b^2 \: = c^2 \\ or. \: a^2+b^2=(97)^2 \\ or. \: a^2+b^2 = 9409………….(3)$

$Formula:-\\ (a-b)^2+(a+b)^2=2(a^2+b^2)\\ or. \: (a-b)^2+(137)^2=2×9409\\ or. \: (a-b)^2+18769=18818 \\ or. \: (a-b)^2=49 \\ or. \: (a-b) = +/-7 m………………(4)$

$Adding \: eqn. \: (2) \: and \: (4) \\ 2.a= \frac{137 + 7}{2} \\ or. \: a = \frac{(137 + 7)}{2} m. or. \frac{(137 - 7)}{2} m. \\ or. \: a = 72 m. \: or. \: 65 m. \: Answer\\ Subtracting \: eqn \: (4) \: from \: (2). \\ 2.b= (137-/+7). \\ or. \: b= (137–7)/2 m. or. (137+7)/2 m. \\ or. \: b = 65 m. or. 72 m. (Answer).$

Answer 2

Answer:

answer is 65 mm

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