Question

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 1

let the base be x
then altitude = x-7
hypotenuse = 13 cm
by pt
 x2+(x–7)2=132
x2+x2+49–14x=169
2x2–14x+48–169=0
2x2–14x–120=0
x2–7x–60=0  
x2–12x+5 x–60=0  
x(x–12)+5(x–12)=0  
(x–12)(x+5)=0 
x=12 or x=–5
as we know that length of triangle can not be negative
base=x= 2cm 
altitude=12–7=5cm

@skb

Answer 2

Hi...
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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