A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.
1 answer:
The side of the edge of the cube is 7. 07cm
<h3>How to determine the length</h3>Given that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square =
a is the side of the square face
We have that,
Make 'a' subject of formula
a =
Find the surd of the equation, we have
a = ×
a =
a =
a =
Thus, the side of the edge of the cube is 7. 07cm
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For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be: centimeters.
Likewise, from the same theorem we have:
