Question

In an isosceles triangle, the length of the base is half of the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.
Only answer required.

Answer 1

To solve this question, we have to:

Understand the concept of an isosceles triangle.

Use this concept, along with the perimeter concept, to build the equation to find the length of the sides.

Doing this, we get that the length of the base is 10 cm and the length of the legs is 20 cm.

Isosceles triangle:

In an isosceles triangle, two sides have the same measure. An example is given by the picture at the end of this answer.

Perimeter:

The perimeter of a polygon, in this case a triangle, is the sum of all it's sides.

In this question:

Perimeter of 50 cm;

Two legs of l;

Base is half the leg, so l/2.

Then, the equation is:

Thus:

The length of the legs is of 20 cm.

The length of the base is of 20/2 = 10 cm

Answer 2

The length of all the sides of an isosceles triangle are needed.

The length of each leg is 20 cm and the base is 10 cm.

Let length of the legs be $a$

The length of the base $b$ is half of one of the legs.

$b=\dfrac{1}{2}a$

Perimeter of triangle is 50 cm.

Perimeter of an isosceles triangle is given by

$P=2a+b\\\Rightarrow P=2a+\dfrac{1}{2}a\\\Rightarrow P=\dfrac{5}{2}a\\\Rightarrow a=\dfrac{2}{5}P\\\Rightarrow a=\dfrac{2}{5}\times 50\\\Rightarrow a=20$

Base

$b=\dfrac{1}{2}a=\dfrac{1}{2}\times 20\\\Rightarrow b=10$

The length of each leg is 20 cm and the base is 10 cm.

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