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.

• A. 2,5
• B. 5,3
• C. 7,2
• D. 12,5

Answer 1

The correct option is D

12,5

Let the base = x cm

Give that the altitude of a right triangle is 7 cm less than its base

Altitude is = x - 7 cm

Given that hypotenuse = 13 cm

Applying Pythagoras theorem,

$bas{e}^2+altitud{e}^2=hypotenus{e}^2$ plug the values we get

$x^2+(x-7{)}^2={13}^2$

$x^2+x^2+49-14x=169$

$2x^2-14x+49-169=0$

$2x^2-14x-120=0$

Divide by 2 to both side to simplify it

$x^2-7x-60=0$

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

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

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

x - 12 = 0 or x + = 5

x = 12 or x = -5

length can not negative so that x can not equal to -5

base x = 12 cm ; altitude = 12 - 7 = 5 cm