Question

extra practice trapezoids and kites example 1 1. lamp shade the lamp - shade shown is a trapezoidal prism. the front face of the lamp is an isosceles trapezoid. kl = 2x + 2, mj = 6x + 2, lm = 5x - 5, and kj = 3x + 1. a. prove x = 3.

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, the non - parallel sides are equal. Here, $KL$ and $MJ$ are the parallel sides and $LM$ and $KJ$ are the non - parallel sides. So, $LM = KJ$.
Set up the equation: $5x−5 = 3x + 1$.

Step2: Solve the equation for x

Subtract $3x$ from both sides:
$5x−3x−5=3x−3x + 1$
$2x−5 = 1$.
Add 5 to both sides:
$2x−5 + 5=1 + 5$
$2x=6$.
Divide both sides by 2:
$\frac{2x}{2}=\frac{6}{2}$
$x = 3$.

Answer:

$x = 3$ is proved as shown above.