Question

The attitude of a right triangle is 7 cm less than its bass. If the hypotenuse is 13cm, find the other two sides [x=12]

Answer 1

Answer :-

Given :- Hypotenuse = 13 cm ;

Altitude is 7 less than base.

To Find :- Base & altitude.

Solution :-

Let the base be x ;

Altitude = x - 17.

By Pythagoras Theorem :-

(Hyp.)² = (A)² + (b)²

-> (13)² = (x - 7)² + (x)²

-> 169 = (x² + 49 - 14x) + x²

-> 169 = 2x² + 49 - 14x

-> 169 - 49 - 2x² + 14x = 0

-> 120 - 2x² + 14x = 0

-> -2x² + 14x + 120

Now, Factorise it ;

-> -2x² + 24x - 10x + 120

-> -2x (x - 12) - 10 (x - 12)

-> (-2x - 10) (x - 12)

-> x - 12 = 0

-> x = 12

So, the base is 12 cm ;

So, the base is 12 cm ;Altitude = 12 - 7 = 5 cm.

Answer 2

☞ The attitude of a right triangle is 7 cm less than its base.

» Let the base (B) of triangle be x cm

• Altitude is 7cm less than its base.

» Altitude = (x - 7) cm

» Hypotenuse = 13 cm

_____________________________

We know that

H² = B² + P²

________ [By Pythagoras theorem]

=> (13)² = (x)² + (x - 7)²

=> 169 = x² + x² + 49 - 14x

=> 169 - 49 = 2x² - 14x

=> 120 = 2x² - 14x

=> 2x² - 14x - 120 = 0

• Take 2 common

=> 2(x² - 7x - 60) = 0

=> x² - 7x - 60 = 0

=> x² - 12x + 5x - 60 = 0

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

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

• x + 5 = 0

=> x = - 5 (side can't be in negative. So, rejected.)

• x - 12 = 0

=> x = 12

_______________________________

• Base of triangle = x = 12 cm

• Altitude of triangle = x - 7 = 12 - 7 = 5 cm

_______________________________

The other two side are 12 cm and 5 cm.

___________ [ANSWER]