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In this video, I solve a right triangle problem where both the perimeter and area are 30. Using the Pythagorean theorem and algebra, I break down the steps to find the sides of the triangle. Watch to learn how to solve this challenging geometry problem!
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find the sides of a right triangle whose
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perimeter and area are equal to 30 as
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usual try to solve the problem on your
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own the perimeter of the triangle by
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definition is equal to the sum of the
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lengths of all its sides and the area of
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the right triangle in this case is equal
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to half the product of its legs
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additionally we will use the Pythagorean
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theorem for this right triangle which
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states that the sum of the squares of
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the legs is equal to the square of the
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hypotenuse to solve the system we will
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try to express the sum of A and B
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through the sum of their squares for
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this we will need to add to the sum of
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the squares of A and B their double
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product which we can find from the
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second equation so from the first
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equation we express the sum of A and B
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and from the second equation we express
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the product of A and B for this both
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sides of the equation need to be
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multiplied by two and to each side of
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the third equation we will add the
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double product of A and B as a result in
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the left part of the Third thir equation
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we get the sum of A and
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B let's solve the third equation of the
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system separately for this we substitute
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from the first equation instead of the
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sum of a and b 30- c and instead of the
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product of A and B we substitute the
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number 60 from the second equation then
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30 - c will be equal to C of 2qu + 2 *
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60 we open the parentheses and subtract
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from both sides of the equation we
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express press and find C then return to
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the system and find A and B from the
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first two equations then the sum of A
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and B will be equal to 30 minus C that
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is 13 the product of A and B is equal to
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60 the system can be solved in different
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ways for example you can express one of
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the variables from the first equation
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and substitute it into the second
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equation or you can recall vieta's
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theorem According to which the numbers A
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and B are the roots of the quadratic
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equation x^ 2 minus the sum of A and B *
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X plus the product of the roots that is
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60 60 is the product of 5 and 12 and 17
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is the sum of the roots 5 and 12 with a
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negative sign so either a = 5 and B = 12
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or a = 12 and B = 5 thus the sides of
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the right triangle are 5 12 and 13 if
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you unod give a like write comments and
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