The altitude of a right triangle is 7cm less than its base . if the hypotenuse is 13cm , find the other two sides
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Let the base be a
Altitude = a - 7
Now,
Hypotenuse = sqrt [ a^2 + (a - 7)^2]
=> 13 = sqrt ( a^2 + a^2 + 49 - 14a)
=> 169 = 2a^2 + 49 - 14a
=> 2a ^2 - 14a - 120 = 0
=> a^2 - 7a - 60 = 0
=> a^2 - 12a + 5a - 60 = 0
=> a(a-12) + 5 (a-12) = 0
=> (a+5)(a-12) = 0
a = - 5 and 12
But length can't be negative, so
=> a =12
Base = 12 cm
Altitude = 12 - 7 = 5 cm
Altitude = a - 7
Now,
Hypotenuse = sqrt [ a^2 + (a - 7)^2]
=> 13 = sqrt ( a^2 + a^2 + 49 - 14a)
=> 169 = 2a^2 + 49 - 14a
=> 2a ^2 - 14a - 120 = 0
=> a^2 - 7a - 60 = 0
=> a^2 - 12a + 5a - 60 = 0
=> a(a-12) + 5 (a-12) = 0
=> (a+5)(a-12) = 0
a = - 5 and 12
But length can't be negative, so
=> a =12
Base = 12 cm
Altitude = 12 - 7 = 5 cm
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