A Cake Is Triangular In Shape. Each Side Measure 1 Foot. If The Cake Is Subdivided Equally Into Two By Slicing From One Corner Perpendicular To The Op
A cake is triangular in shape. Each side measure 1 foot. If the cake is subdivided equally into two by slicing from one corner perpendicular to the opposite side,how long is that edge where the cake is sliced?
Answer:
0.866 ft
Step-by-step explanation:
TRIANGLES are three sided polygons by which the sum of its interior angle is equal to 180 degrees.
Let us look at the problem.
Since the problem is telling us that all the sides of the triangular cake are equal measuring 1 foot each, then we can say that the triangle is an EQUILATERAL TRIANGLE.
The problem further says that the cake is divided into two equal parts.
See provided illustration for reference.
From the tip of the triangular cake, we cut the cake into half, making a 90 degree angle to the base of the cake.
Basing on the illustration we have, we created another triangle which is smaller than the original cake.
The phrase "how long is that edge" refers to the length of the side by which the cake is sliced into two.
Using the PYTHAGOREAN THEOREM, which is described by the formula below, we can now solve the unknown.
c^2 = a^2 + b^2
Substituting the values to the equation, having
c = 1 foot;
a = 0.5 foot; and
b = unknown
we have.
(1 ft)^2 = (0.5 ft)^2 + (b^2)
1 ft^2 = (0.25 ft^2) + b^2
Transposing the values, we have
b^2 = 1 ft^2 - 0.25 ft^2
b^2 = 0.75 ft^2
Getting the square of both sides
b = 0.866 ft
Therefore, the length of the edge where the cake is sliced is 0.866 ft.
For more related problems about triangles, see links below.
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