A 41-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than five times the length of the first piece. Find the lengths of the pieces.

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

Step-by-step explanation:

Given that:

Length of piece of steel = 41 inch

Let,

x be the length of first piece

y be the length of second piece

z be the length of third piece

According to given statement;

x+y+z = 41          Eqn 1

y = 2x                Eqn 2

z = 5x+1            Eqn 3

Putting value of y and z from Eqn 2 and 3 in Eqn 1

Dividing both sides by 8

Putting x=5 in Eqn 2 and 3

y = 2(5) = 10

z = 5(5) + 1 = 25+1 = 26

Hence,

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.