Question

The perimeter of an isosceles triangle is 30 cm. The length of each congruent side is 3 cm more than the length of its base. Find the length of all three sides.

Answer 1

Hint: An isosceles triangle is a triangle with two of its sides equal. Relate the length of the base to the congruent sides. Then solve for the sides using the perimeter of the triangle.

Complete step-by-step answer:
An isosceles triangle is a triangle that has two sides of equal length. The two corresponding angles of the isosceles triangle are also equal.
Let the length of the equal sides be x and the length of the other side be y.
It is given that the length of the base is 3 cm shorter than the length of the congruent sides. Hence, we have the following:
\[y = x - 3..........(1)\]
The perimeter of a figure is defined as the length of the path that surrounds an area. For a polygon, it is the sum of its sides.
The perimeter of a triangle is the sum of all the three sides.
The perimeter is given to be 30 cm, hence, we have:
\[x + x + y = 30...........(2)\]
Substituting equation (2) in equation (1), we have:
\[x + x + x - 3 = 30\]
Simplifying the equation, we have:
\[3x - 3 = 30\]
Solving for x, we have:
\[3x = 30 + 3\]
\[3x = 33\]
\[x = \dfrac{{33}}{3}\]
\[x = 11cm\]
Hence, the values of the equal sides are 11 cm each.
Substituting x in equation (1), we have:
\[y = 11 - 3\]
\[y = 8cm\]
Hence, the lengths of the sides are 11 cm, 11 cm, and 8 cm.

Note: Do not conclude after finding the length of the equal sides. You are asked to find the length of all three sides. Hence, you need to find both the length of equal sides and the base.