The base of an isosceles triangle and one of its legs have lengths that have consecutive integers. The leg is longer than the base. The perimeter of the triangle is 20. Find the length of each side of the triangle.
*Please help me- I am having a really bad day. Thank you.*
Let the base be x units long.
"Consecutive integers" are one apart, so if the first one is x then the next one must be x+1.
So the other two sides must be x+1 each.
Since perimeter is the sum of the 3 sides...
x + x+1 x + x+1 = 20
3x + 2 = 20
3x=18
x=6
So the base is 6 and each of the other two sides is 7
check: 6 and 7 are consecutive integers
6+7+7 = 20
x + x+1 x + x+1 = 20
In the above, where did you get the 1x from? This is what I came out with:
x+x+x+1=20
It was clearly a typo
looking at the line that follows should have made it obvious.
this is what it should have been putting the sides in brackets
(x) + (x+1) + (x+1) = 20
ok I get it. I got x= 6 now i can go from there. Thanjs much for all your help!
Would the let statements go like this then:
Let x= 1st C.I.= 6
Let x+1= 2nd C.I.= 7
Let x+1= 3rd C.I.= 7
b/c the second and 3rd aren't C.i.s, so...????????
Read the question carefully.
You said the triangle was isosceles, so two of its sides have to be the same.
yeah, but how do i convey that in the let statements? 7=7, so they aren't consec. integers, right? if so, what do i put instead?
i don't know the answer
I'm sorry to hear that you're having a bad day, but I'll do my best to help you with this problem! Let's break it down step by step.
First, let's assign some variables to represent the lengths of the base and one of the legs of the triangle. Since the base and leg have consecutive integer lengths, we can call the length of the base "x" and the length of the leg "x + 1".
Next, we need to write an equation based on the given information. The perimeter of the triangle is the sum of all its sides, so we can set up the equation as follows:
Perimeter = Base + Leg + Leg
20 = x + (x + 1) + (x + 1)
Now, let's simplify the equation:
20 = x + x + 1 + x + 1
Combining like terms:
20 = 3x + 2
To isolate "x", we subtract 2 from both sides of the equation:
20 - 2 = 3x + 2 - 2
18 = 3x
Next, divide both sides of the equation by 3 to solve for "x":
18/3 = 3x/3
6 = x
Now that we know the length of the base (x = 6), we can find the lengths of the other sides by substituting the values back into the equation. The length of the leg is x + 1, so we add 1 to the value of x:
Leg = 6 + 1
Leg = 7
Finally, we can find the length of the other leg by adding the base and leg:
Other Leg = Base + Leg
Other Leg = 6 + 7
Other Leg = 13
Therefore, the lengths of the sides of the isosceles triangle are 6, 7, and 13.
I hope this explanation helps, and I hope your day gets better! If you have any other questions, feel free to ask.