knr3404
contestada

the perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenuse.
a) 6 ft, 12ft
b) 5 ft, 13 ft
c) 8 ft, 10 ft
d) 7 ft, 11 ft

the perimeter of a right triangle is 24 ft and one of its legs measures 6 ft Find the length of the other leg and the hypotenuse a 6 ft 12ft b 5 ft 13 ft c 8 ft class=

Respuesta :

wilmaralzate

Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

[tex]h^2= a^2+b^2.[/tex]

and the perimeter is [tex]P=h+a+b[/tex].

Since P=24 and a=6  we have these equations:

[tex]h^2=36+b^2\\24=h+6+b[/tex]

From the last equation we have [tex]h=18-b[/tex]. Replace h in the first equation we get that

[tex](18-b)^2=36+b^2[/tex]

[tex]18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8[/tex]

and h=18-8=10

Otras preguntas