Name: The Angle Sum Property of Triangle: Example
Uploaded: 2019-07-19
Duration: 4 min 2 s
Description: How would we find the third angle of a triangle if the other two angles are known? Well, we already know that the sum of the three angles is always 180 degre...

Question

A wire of length

18 cm

is bent to form an isosceles triangle of integral sides. Give the measures of sides of three possible isosceles triangles that can be bent with the wire.

Accepted Answer

An isosceles triangle has two sides equal.

Given that the sides of the required triangles must have integral values.

The perimeter (the sum of all the sides) of all the triangles must be equal to the length of the wire, which is $18 cm$ .

We shall explore the different combinations of the sides of the isosceles.

$17 cm + 0.5 cm + 0.5 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$16 cm + 1 cm + 1 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$15 cm + 1.5 cm + 1.5 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$14 cm + 2 cm + 2 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$13 cm + 2.5 cm + 2.5 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$12 cm + 3 cm + 3 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$11 cm + 3.5 cm + 3.5 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$10 cm + 4 cm + 4 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$9 cm + 4.5 cm + 4.5 cm = 18 cm$ -- not possible to form a triangle because the sum of the smaller two sides is not greater than the third side.

$8 cm + 5 cm + 5 cm = 18 cm$ -- possible.

$7 cm + 5.5 cm + 5.5 cm = 18 cm$ -- not possible because $5.5$ is not an integer.

$6 cm + 6 cm + 6 cm = 18 cm$ -- not possible because it is not an isosceles triangle. It is an equilateral triangle.

$5 cm + 6.5 cm + 6.5 cm = 18 cm$ -- not possible because $6.5$ is not an integer.

$4 cm + 7 cm + 7 cm = 18 cm$ -- possible

$3 cm + 7.5 cm + 7.5 cm = 18 cm$ -- not possible because $7.5$ is not an integer

$2 cm + 9 cm + 9 cm = 18 cm$ -- possible

$1 cm + 8.5 cm + 8.5 cm = 18 cm$ -- not possible because $8.5$ is not an integer.

Hence, the three isosceles triangles that are possible have the dimensions $(8 cm, 5 cm, 5 cm); (4 cm, 7 cm, 7 cm)$ and $(2 cm + 8 cm + 8 cm)$ .

A wire of length $18 cm$ is bent to form an isosceles triangle of integral sides. Give the measures of sides of three possible isosceles triangles that can be bent with the wire.

Important Questions on Triangle and Its Properties

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