Question

the hypotenuse of a right angle triangle is 13cm long if the base of the triangle is 7cm more than the other side then find the other the other two sides
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Answer 1

Answer:

Let the perpendicular of the right angled triangle be x cm,

Then the base of the right angled triangle= (x+7)cm

ATQ:-

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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