Respuesta :
Let 'x' denote the length of the base and let 'y' denote the length of the legs.
We know that isosceles triangles have one base and two legs that are the same length. So, the perimeter is:
x+y+y
= x+2y = 50
The problem tells us that the base is half as long as a leg, so that means:
y=2x
We can use the method of substitution here. Let's substitute the 2nd given equation into the first one. The work follows:
x+2y=50
x+2(2x)=50
x+4x=50
5x=50
x=50/5
x=10
To work out what the length of our legs are, we can use our found 'x' value to solve either of our previously established equations. Let's use the second one:
y=2x
y=2(10)
y=20
Just to confirm our answer is correct, let's verify it with our first equation.
x+y+y=50
10+20+20=50
50=50
Our answer is consistent, so the base has length 10, and each leg has length 20.
We know that isosceles triangles have one base and two legs that are the same length. So, the perimeter is:
x+y+y
= x+2y = 50
The problem tells us that the base is half as long as a leg, so that means:
y=2x
We can use the method of substitution here. Let's substitute the 2nd given equation into the first one. The work follows:
x+2y=50
x+2(2x)=50
x+4x=50
5x=50
x=50/5
x=10
To work out what the length of our legs are, we can use our found 'x' value to solve either of our previously established equations. Let's use the second one:
y=2x
y=2(10)
y=20
Just to confirm our answer is correct, let's verify it with our first equation.
x+y+y=50
10+20+20=50
50=50
Our answer is consistent, so the base has length 10, and each leg has length 20.
