Question

1. find the value of d, show your work for full credit!!! type a response

Explanation:

Step1: Use property of isosceles triangle

Since $AB = BC=60$, triangle $ABC$ is isosceles. And $BD\perp AC$, so $AD = DC$ (perpendicular from vertex to base in isosceles triangle bisects the base). Then $6d + 3=10d-25$.

Step2: Solve the equation for d

Subtract $6d$ from both sides: $3 = 10d-6d - 25$, which simplifies to $3 = 4d-25$.
Add 25 to both sides: $3 + 25=4d$, so $28 = 4d$.
Divide both sides by 4: $d=\frac{28}{4}=7$.

Answer:

$7$