Question

the altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm, find the other two sides ​

Answer 1

Answer:

other sides are 12 cm , 5 cm

Explanation:

let the base = x cm

so altitude is = x - 7 cm

using pythagores theorem

(hypotenous)² = (base)² + (altitude)²

(13)² = (x)² + (x - 7)²

169 = x² + x² + 49 - 14x

2x² - 14x + 49 - 169 = 0

2x² - 14x - 120 = 0

divide by 2

x² - 7x - 60 = 0

using middle term

x² - (12 - 5)x - 60 = 0

x² - 12x + 5x - 60 = 0

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

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

x - 12 = 0 . x + 5 = 0

x = 12 . x = -5

sides are not be negative

so. base of triangle = 12 cm

and altitude is = 12 - 7 = 5 cm

Answer 2

Answer:12and5

Explanation

Let the base=x

Altitude=x-7

Hypotenuse =13cm

Hypo2=base2+alti2

Sorry balance cant be written keyboard problem.

Last stepx(x-12)5(x-12)

X=12, x=5