word prob.?

Question

two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find the lengths of the sides of the triangles if their perimeters are 23cm and 41cm.

explaining it to me would be very helpful guys! thanks so much!

Answer 1

x + x + y = 23
2x + 2x + y = 41

where x represents the legs of the smaller triangle and 2x the larger.

Simplifying

2x + y = 23
4x + y = 41

Subtract the top equation from the bottom

2x = 18

so x = 9 and 2x = 18

so the smaller triangle has sides 9, 9, and 5
and the larger's is 18, 18, and 5

Answer 2

Hello Lauren:

This one is a simple one to work out.

Iscsceles means two sides the same length.
Problem said the bases of both triangles are the same.

So if Perimeter = Side 1 + Side 2 + Base = 23 cm
then write that as 2X + Y = 23

and for the other triangle whose sides are twice as long as those of the first triangle, that would be written:
2X + 2X + Y = 41 cm

so we have:

2X + Y = 23
4X + Y = 41

Solve for "Y" in the first equation...

Y = 23 - 2X

Now insert the solution for "Y" into the second equation...

4X + 23 - 2X = 41 and solve for "X"

So: 2X + 23 = 41
2X = 41 - 23
2X = 18
X = 9 cm

If X = 9, then, from the first equation we can solve for "Y"

2X + Y = 23 cm
2(9) + Y = 23 cm
18 + Y = 23
Y = 23 - 18
Y = 5 cm

Check: 2(9) + 5 = 23.......checks good
4(9) + 5 = 41.......checks good
Solved.
Cheers,
Zah

Answer 3

psh, simple. lol if both bases are the same, set the base as the letter B= Base. Then the legs of the shorter triangle can be L=Legs. So the perimeter of the small triangle should be B+L+L = 23. The Larger triangle would be B+2L+2L = 41. Solve the first equation for B and you get B = 23 - 2L. Substitute that into the second equation and (23-2L) + 4L = 41. => 2L = 18 => L = 9. If L = 9, then B+9+9 = 23, B = 5. The smaller triangle's side lengths are 5-9-9. The larger, 5-18-18.

Answer 4

You know that the base of each triangle is the same. Let's call the base x.

Now since the triangles are isosceles you know that the sides of each are the same, so let y be the sides of one and z the sides of the other.

Now we have two equations for the perimeters:

x+2y=23 and
x+2z=41

Suppose the triangle that has the longer sides is the triangle with the zs. You are given a relation between the two triangles, namely that the legs of one are twice as long as the other. This gives us the equation:

2y=z, now substitute this in for z and you get two equations in two unknowns:

x+2y=23
x+2*(2y)=41 or x+4y=41

Since there are two equations with only one x, you could subtract one equation from the other to get a value for y. Alternatively you could isolate an x (x=.......) and substitute this into the other equation. Use this to find the other two values.

I hope this helps.

Answer 5

Perimeter of triangle 1

X + X + y = 23 (Y is the base, X equals sides)

Perimeter of triangle 2

2X + 2X + y = 41 (twice the length gives 2X, y = same base as triangle 1)

2 equations, 2 unknowns, solve for them

X= 9 and Y =5

good luck chief

Answer 6

You also know from what the previous poster wrote that 2x + y = 23 & 2x + 2x +y = 41.

You can substitute the first equation into the second equation. To clarify:

2x + (2x + y) = 41 (Since we know that 2x + y = 23, we can replace variables in parentheses).

2x + 23 = 41
2x + 23 -23 = 41-23
2x = 18
x = 9.

Substitute back into the equation:

2(9) + y = 23
18 + y = 23
18 - 18 + y = 23 -18
y = 5, therefore,

x = 9, y = 5.

In questions such as this, once you've solved for all variables, check your math by substituting the numbers into the second equation.

2(9) + 2(9) + 5 = 41
18 + 18 + 5 = 41
36 + 5 = 41
41 = 41

Answer 7

fill in the information that you know into the perimeter equation and then solve from there.

Answer 8

~~~ouch,,,my head hurts now,,,,need to go do a shot of some "Crown Royal" ,,,, So glad Im not in school anymore!! ~~~

Answer 9

You explain it