Question

The perimeter of an isosceles triangle is $15.6\mathrm{m}$. Find the lengths of its sides, if the base is $3m$ bigger than a leg.

Answer 1

Step-1: Find the length of the sides:

Let the leg of the triangle is $x$.

Since the given triangle is an isosceles triangle. Thus, the two sides of the triangle are equal.

Thus, the other leg of the triangle is $x$.

Since it is given that the base is $3\mathrm{m}$ bigger than the leg.

Thus, the base of the triangle is $x+3$.

Step-2: Find the value of $x$:

Since the perimeter of the triangle is $15.6\mathrm{m}$.

Thus, the sum of all the sides of the triangle is $15.6\mathrm{m}$.

$\begin{array}{rcl}x+x+x+3& =& 15.6\\ & \Rightarrow & 3x+3=15.6\\ & \Rightarrow & 3x+3-3=15.6-3\left[\text{Subtract 3 from both sides of the equation}\right]\\ & \Rightarrow & 3x=12.6\\ & \Rightarrow & \frac{3x}{3}=\frac{12.6}{3}\left[\mathrm{Divide}\mathrm{both}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{equation}\mathrm{by}3\right]\\ \therefore x& =& 4.2\end{array}$

Thus, the leg of the isosceles triangle is $4.2\mathrm{m}$.

Step-3: Find the value of the base:

Since the length of the base is $x+3$.

Put the value of $x$ in $x+3$ to obtain the base of the triangle.

$$\begin{gathered} x+3=4.2+3 \\ \therefore x+3=7.2\text{m} \end{gathered}$$

Hence, the length of two equal sides and base of the triangle are $4.2\mathrm{m}$ and $7.2\mathrm{m}$ respectively.