Question

on republic day a poster is to be made by class 10 students of a school. all religions have been given equal right triangular spaces to display their teachings. hypotenuse of the right triangle is 25 cm and out of the remaining two sides, one is longer that the other by 5 cm. find the lengths of the other two sides

Answer 1

This is your answer with step by step explanations

Answer 2

Step-by-step explanation:

one side = x

and other side = x + 5

hypotenuse = 25

by Pythagoras theorem

${hypotenuse}^{2} = {base}^{2} + {hight}^{2} \\ {25}^{2} = {x}^{2} + {(x + 5)}^{2} \\ 625 = {x}^{2} + {x}^{2} + {5}^{2} + (2 \times 5 \times x) \\ 625 = 2 {x}^{2} + 25 + 10x \\ 2( {x}^{2} + 5x) = 625 - 25 \\ {x}^{2} + 5x = \frac{600}{2} \\ {x}^{2} + 5x = 300 \\ 5x = 300 - {x}^{2} \\ x = \frac{300 - {x}^{2} }{5}$

$length \: of \: first \: side \: is \: \frac{300 - {x}^{2} }{5}$

$length \: of \: second \: side \: is \: \\ \frac{300 - {x}^{2} }{5} + 5 \\ = \frac{300 - {x}^{2} + 25 }{5} (by \: taking \: lcm) \\ = \frac{325 - {x}^{2} }{5}$

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