Question

Given: Isosceles ABC with vertex angle B;

AB = 5x + 10; BC = 3x + 40; AC = 2x + 30
a. Draw an appropriately labeled picture.
b. x = __________
c. AB = __________
d. BC = __________
e. AC = __________"

Answer 1

To solve for x, we can equate either AB or AC to their given values. Plugging x = 4 into AB, BC, and AC, we can find the lengths of each side: AB = 30, BC = 52, and AC = 38.

Step-by-step explanation:

Given: Isosceles triangle ABC with vertex angle B; AB = 5x + 10; BC = 3x + 40; AC = 2x + 30.

1. To draw an appropriately labeled picture, we can start by drawing a triangle with two equal sides AB and AC, and angle B as the vertex angle.
2. x can be found by equating either AB or AC to the given value and solving for x. Let's use AB = 5x + 10. If AB = 5x + 10, then 5x + 10 = 5(x) + 10 = 5x + 10 = 5x + 10 = 30. Solving for x, we get x = 4.
3. Plugging x = 4 into AB, we get AB = 5(4) + 10 = 20 + 10 = 30.
4. Plugging x = 4 into BC, we get BC = 3(4) + 40 = 12 + 40 = 52.
5. Plugging x = 4 into AC, we get AC = 2(4) + 30 = 8 + 30 = 38.