the altitude of a right angle triangle is 7 cm less than its base . If the hypotenuse is 13 cm . Find the other two sides . Also write perimeter of given triangle..
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Answered by
1
Let the base be a
Altitude = a - 7
Hypotenuse = 13 cm
By pythagores theorem,
(13)^2 = (a-7)^2 + (a)^2
=> 169 = a^2 - 14a + 49 + a^2
=> 169 = 2a^2 - 14a + 49
=> 2a^2 - 14a - 120 = 0
=> a^2 - 7a - 60 = 0
=> a^2 - 12a +5a - 60 = 0
=> a ( a - 12) + 5(a - 12) = 0
=> (a-12)(a + 5) = 0
a = 12 and - 5
But length of side can't be negative, so
a = 12
Base = 12 cm
Altitude = 12 - 7 = 5 cm
Altitude = a - 7
Hypotenuse = 13 cm
By pythagores theorem,
(13)^2 = (a-7)^2 + (a)^2
=> 169 = a^2 - 14a + 49 + a^2
=> 169 = 2a^2 - 14a + 49
=> 2a^2 - 14a - 120 = 0
=> a^2 - 7a - 60 = 0
=> a^2 - 12a +5a - 60 = 0
=> a ( a - 12) + 5(a - 12) = 0
=> (a-12)(a + 5) = 0
a = 12 and - 5
But length of side can't be negative, so
a = 12
Base = 12 cm
Altitude = 12 - 7 = 5 cm
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Answered by
2
Let the base be a
Altitude = a - 7
Hypotenuse = 13 cm
By pythagores theorem,
(13)^2 = (a-7)^2 + (a)^2
=> 169 = a^2 - 14a + 49 + a^2
=> 169 = 2a^2 - 14a + 49
=> 2a^2 - 14a - 120 = 0
=> a^2 - 7a - 60 = 0
=> a^2 - 12a +5a - 60 = 0
=> a ( a - 12) + 5(a - 12) = 0
=> (a-12)(a + 5) = 0
a = 12 and - 5
But length of side can't be negative, so
a = 12
Base = 12 cm
Altitude = 12 - 7 = 5 cm
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