Step-by-step explanation:
there are 2 similar triangles : ABE and DCE
that means they have the same angles, and the scaling factor from one triangle to the other is the same for every side.
and that means that
DE/AE = EC/BE (= DC/AB)
we know that
AE = AD + DE
BE = BC + EC
a.
so, we have actually
DE/(AD+DE) = EC/(BC+EC)
DE/(10+DE) = 8/(2+8) = 8/10 = 4/5
DE = 4(10+DE)/5
5DE = 4(10+DE) = 40 + 4DE
DE = 40 cm
b.
AD/DE = 3/5
BC/EC must be 3/5 too.
15/EC = 3/5
15 = 3EC/5
75 = 3EC
EC = 25 cm
<span>First, calculate the difference between 15 and 12. The operation, subtraction, will give us the answer of 3. Then, divide the calculated value by 12 since this it the theoretical length of the nail. Multiply the quotient by 100% to arrive to the final answer. That is (3/12)(100%). The final answer to this item is 25% which is the last choice. </span>
Answer: It equals 8.
Step-by-step explanation: