Remi is building a triangular wooden shelving unit. the base measures 30 cm and the slant sides measure 18 cm and 24 cm. he wants a horizontal shelf halfway between the bas and the top. what length of wood should he cut for the shelf?

Remi needs 15 cm of wood to be cut for the shelf.

Step-by-step explanation:

We have drawn the triangle for your reference.

Now Given:

Base measure (BC) =30 cm

Slant height (AB) = 24 cm

Slant height (AC) = 18 cm

Also Given horizontal shelf halfway between the base and the top.

In the triangle drawn horizontal shelf is denoted by DE.

We need to find the measure of DE.

Now we know that horizontal shelf halfway between the base and the top.

Hence by Midpoint theorem which states that;

"The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side."

Substituting the value we get;

Hence Remi needs 15 cm of wood to be cut for the shelf.

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value