Math Problem...i need some help...please?

Question

Its a word problem, and it says:

A triangle has two sides equal in length and a third side 5in. longer than half the length of each of the other two sides. If the perimeter of the triangle is 50in, How long is each side?

I just cant figure it out, the instructions say to "Write an equation, and solve"
i dont just want the answer, i just want to know how to do it...

thank you!
-much love- Ashley

Answer 1

So it might help you to draw a picture.

A. Draw a triangle.

B. First it says that 2 sides are equal in length. Say those are both equal to "x".

C. The third side then says that it is equal to one half of one of the sides (x) plus 5.
you can say that side is

0.5x + 5

D. Then it says that the perimeter (all the sides added together) equal 50. You can then say that

50= x + x + .5x + 5
simply that equation to say
50=2.5x + 5

E. Then just solve for x. subtract 5 from both sides then divide by 2.5.

50 -5 = 2.5x + 5 -5
45=2.5x
45/2.5=2.5x/2.5
18= x

D. That, however, only gets you part of the way there. You now know how long 2 of the sides are, but you still need to know the other one. Using the expression we made above (0.5x + 5), substitute 18 in for x, then solve to find the value of the final side of the triangle.

.5(18) + 5
9 + 5
14

So your answers should be:
18,18, and 14

Answer 2

Remember that the perimeter of a triangle is calculated by:

P = a + b + c

Where a, b, and c are the sides of the triangle.

We're given that two of the sides are equal in length. Therefore, a = b, and

P = b + b + c
P = 2b + c

We're also given that the third side (which, in our case, is c) is 5 inches longer than half the length of the other two sides. This means

c = (1/2)b + 5, since

"The third side (c) is (=) 5 inches longer (+5) than half the length (1/2 * b) of the other two sides."

Since P = 2b + c, we now know what c is, so

P = 2b + (1/2)b + 5

But we know that P = 50, so

50 = 2b + (1/2)b + 5

You seem to genuinely want to know how to do it, so I'll stop right here and hope that this helped.

Answer 3

Each of 2 equal sides = x
Third side = x / 2 + 5

Perimeter
x + x + x/2 + 5 = 50
Multiplying both sides by 2
2x + 2x + x + 10 = 100
5x + 10 = 100
Subtracting 10 from both sides
5x = 90
x = 90/5 = 18

Third side = x/2 + 5 = 18/2 + 5 = 9 + 5 = 14

18", 18" and 14"

Answer 4

s + s + (s/2 + 5) = 50. This reduces to 2.5 s = 45, or s = 18. Nothing complicated here.