Question

3. Multiple Choice: The lengths of the two legs of an isosceles triangle are represented by the expressions

2x-5 and x + 7. The perimeter of the triangle is 50cm. Find the length of the base of the triangle.
(FYI: The "legs" are the 2 congruent sides of an isosceles triangle. The "base" is the noncongruent side.),
(A) 11cm
(B) 19cm
(C) 12cm
(D) 26cm
(E) 32cm

Answer 1

The length of the base of the isosceles triangle is 19 cm.

Step-by-step explanation:

To find the length of the base of the isosceles triangle, we need to use the fact that the perimeter of a triangle is the sum of the lengths of its sides. The perimeter formula for this triangle is (2x - 5) + (x + 7) + (x + 7) = 50. Simplifying the equation, we get 4x + 9 = 50. Solving for x, we find x = 10. Substituting the value of x back into the expression for the length of the base, the length of the base is (10 + 7) cm = 17 cm. Therefore, the correct option is (B) 19 cm.

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