Question

Given: AACD is isosceles with angle D as the vertex angle. B is the midpoint of AC. AB= x + 5, BC= 2x - 3, and CD = 2x + 6. Find the perimeter of ∆ACD.​

Answer 1

• 70 units

Explanation:

Given triangle ACD

• AB = BC
• CD = 2x + 6
• AB = x + 5
• BC = 2x - 3
• P = ?

Perimeter is sum of the side lengths:

• P = AD + CD + AC

AD = CD because D is vertex and the triangle is isosceles

AC = AB + BC because B is midpoint of AC

Then P is:

• P = 2(2x + 6) + (x + 5) + (2x -3) = 4x + 12 + x + 5 + 2x - 3 = 7x + 14

Find the value of x from the AB = BC:

• x + 5 = 2x - 3
• 2x - x = 5 + 3
• x = 8

Then find the value of P:

• P = 7*8 + 14 = 56 + 14 = 70 units