Question

determine the perimeter of $\triangle jkl$. the triangle is not drawn to scale.

$jk=(9x + 1)\text{ m}$

$kl=(6x + 7)\text{ m}$

$jl = 29\text{ m}$

Explanation:

Step1: Use the property of isosceles triangle

Since $\angle J=\angle L$, then $\triangle JKL$ is isosceles and $JK = KL$.
$$9x + 1=6x + 7$$

Step2: Solve for $x$

Subtract $6x$ from both sides:
$$9x-6x + 1=6x-6x + 7$$
$$3x+1 = 7$$
Subtract $1$ from both sides:
$$3x+1 - 1=7 - 1$$
$$3x=6$$
Divide both sides by $3$:
$$x = 2$$

Step3: Find the lengths of $JK$ and $KL$

Substitute $x = 2$ into $JK=9x + 1$:
$$JK=9\times2+1=19$$
Substitute $x = 2$ into $KL=6x + 7$:
$$KL=6\times2+7 = 19$$

Step4: Calculate the perimeter

The perimeter $P$ of $\triangle JKL$ is $P=JK + KL+JL$.
$$P=19 + 19+29$$
$$P=67$$

Answer:

$67$ m