Question

the hypotenuse of a right triangle is 5 ft long. the shorter leg is 1 ft shorter than the longer leg. find the side lengths of the triangle

Answer 1

the hypotenuse of the right angle triangle is h = 5 ft

it is given that

the shorter leg is 1 ft shorter than the longer leg.

let the shorter leg is a and longer leg is b

the

b - a = 1

b = 1 + a

in the traingle using Pythagoras theorem,

`a^2+b^2=h^2`

put he values,

`a^2+(1+a)^2=5^2`
`\begin{gathered} a^2+1+a^2+2a=25 \\ 2a^2+2a-24=0 \\ a^2+a-12=0 \end{gathered}`
`\begin{gathered} a^2+4a-3a-12=0_{} \\ a(a+4)-3(a+4)=0 \\ (a+4)(a-3)=0 \end{gathered}`

a + 4 = 0

a = - 4

and

a - 3 = 0

a = 3

so, the longer leg is b = a + 1 = 3 + 1 = 4

thus, the answer is

shorter leg = 3 ft

longer length = 4 ft

hypotenuse = 5 ft