Question

In the diagram, NP=8
inches, and LR=20
inches. What is the diameter of the bottom layer of the cake?

Answer 1

can you provide the diagram for this question

Answer 2

Given :- In the diagram, NP = 8 inches, and LR = 20 inches. What is the diameter of the bottom layer of the cake ?

Solution :-

we know that,

• Trapezoid mid-segment theorem :- The theorem states that the length of the midsegment of a trapezoid is half of the sum of the length of the bases.

so, In Trapezoid NPRL we have,

→ MQ = Mid - segment .

→ NP = 8 inches .

→ LR = 20 inches.

then,

→ MQ = (1/2)(NP + LR) { Trapezoid mid-segment theorem .}

→ MQ = (1/2)(8 + 20)

→ MQ = (1/2) * 28

→ MQ = 14 inches.

therefore , we can conclude that,

• NP + 6 = 8 + 6 = 14 inches = MQ .
• MQ + 6 = 14 + 6 = 20 inches = LR .
• LR + 6 = 20 + 6 = 26 inches = KS.

Hence, the diameter of the bottom layer of the cake is 26 inches.