Given that triangle ABC is congruent to triangle RST, AB=x, BC=x+2, AC=x+4 and RS=2x-7, find the perimeter for triangle ABC.
To find the perimeter of triangle ABC, we need to add up the lengths of its three sides: AB, BC, and AC.
Given that triangle ABC is congruent to triangle RST, this means that their corresponding sides are equal in length. So we can write the following equations based on the given information:
AB = RS (corresponding sides are equal)
BC = ST (corresponding sides are equal)
AC = RT (corresponding sides are equal)
From the given information, we have AB = x and RS = 2x-7. Since AB = RS, we can set up the equation:
x = 2x-7
To solve for x, let's isolate the x term:
x - 2x = -7
Simplifying, we get:
- x = -7
Now, we can solve for x by multiplying both sides of the equation by -1:
x = 7
Therefore, in triangle ABC, AB = x = 7.
Now that we know the value of x, we can find the lengths of BC and AC:
BC = x + 2 = 7 + 2 = 9
AC = x + 4 = 7 + 4 = 11
Finally, we can calculate the perimeter of triangle ABC by adding the lengths of its sides:
Perimeter of ABC = AB + BC + AC
= 7 + 9 + 11
= 27
So, the perimeter of triangle ABC is 27 units.
RS = AB
x = 2x + 7
x = -7