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

Step-by-step explanation:

Let the base be 'a'. So, altitude = 7 cm less than 'a'.

Base = a

Altitude = a - 7

Using Pythagoras theorem,

=> base² + altitude² = hypotenuse²

=> a² + (a - 7)² = 13²

=> a² + (a² + 7² - 2(7*a)) = 169

=> a² + a² + 49 - 14a - 169 = 0

=> 2a² - 14a - 120= 0

=> a² - 7a - 60 = 0

=> a² - 12a + 5a - 60 = 0

=> a(a - 12) + 5(a - 12) = 0

=> (a - 12)(a + 5) = 0

=> a = 12. Or a = - 5, as it cant be -ve, a = 12

Therefore,

base = 12 cm

altitide = 12 - 7 = 5 cm

Answer 2

Answer:

Altitude=5cm

Base=(5+7)cm=12cm

Step-by-step explanation:

x^2+(x+7)^2=(13)^2

=. 2x^2+14x-120=0

=. x^2+7x-60=0

=. (x+12)(x-5)=0. [WHERE, x=altitude,(x+7)=base]

Therefore,

x=5 and x= -12

But, x#12

Then, x=5.