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
