Q5: The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Answer: Let the base = x cm
Given that The altitude of a right triangle is 7 cm less than its base
Altitude is = x - 7 cm
Given that hypotenuse = 13cm
Applying Pythagoras theorem,
base2+ altitude2 = hypotenuse2
plug the values we get
x2+ ( x – 7)2 = 132
x2+ x2+ 49 – 14 x = 169
2 x2– 14 x + 48 – 169 = 0
2 x2– 14 x – 120 = 0
Divide by 2 to both side to simplify it
x2 – 7 x – 60 = 0
x2– 12 x + 5 x – 60 = 0
x ( x – 12) + 5 ( x – 12) = 0
( x – 12)( x + 5) = 0
x – 12 = 0 or x + 5 = 0
x = 12 or x = –5
length can not negative so that x can not equal to – 5
base x = 12cm
altitude = 12 – 7 = 5cm
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