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.

plz answer​

Answer 1

Step-by-step explanation:

Let the base of the triangle be x cm

Then its altitude =x-7.

Hypotenuse =13cm

By pythagoras theorem

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

x^2+x^2+7^2-14x=169

2x^2+49-14x=169

2x^2-14x=120

2x^2-14x-120=0

x^2-7x-60=0

x^2-12x+5x-60=0

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

x=12 x=-5

Since the base cannot be negative, base is 12 cm. The altitude is 12-7=5cm.

Answer 2

Answer

Let base be x

Therefore, altitude=x-7

Now,by pythagorus theorem,

∴(AC)²=(AB)² +(BC)²

∴(13)²=(x)²+(x-7)²

∴169=x²+x²-14x+49

∴x²+x²-14x+49-169=0

∴2x²-14x-120=0

∴2(x²-7x-60)=0

∴x²-12x+5x-60=0

∴x(x-12)+5(x-12)=0

∴(x-12) (x+5)

∴x=12 ; x=(-5)

As (-5) cannot be altitude,

∴x-7

∴12-7

∴5

∴Base=12 and altitude=5

Step-by-step explanation: