a picture frame has a perimeter of 100 cm. its width is 4 cm less than twice its length. what is the width…

Explanation:

Step1: Define variables

Let the length of the picture - frame be $l$ cm and the width be $w$ cm. We know that $w = 2l-4$ and the perimeter formula for a rectangle is $P = 2(l + w)$. Given $P = 100$ cm.

Step2: Substitute $w$ into the perimeter formula

Substitute $w = 2l - 4$ into $P=2(l + w)$: [ \begin{align*} 100&=2(l+(2l - 4))\ 100&=2(3l - 4)\ 100&=6l-8 \end{align*} ]

Step3: Solve for $l$

Add 8 to both sides of the equation: [ \begin{align*} 100 + 8&=6l-8 + 8\ 108&=6l \end{align*} ] Divide both sides by 6: $l=\frac{108}{6}=18$ cm.

Step4: Solve for $w$

Substitute $l = 18$ into $w = 2l-4$: [ \begin{align*} w&=2\times18-4\ w&=36 - 4\ w&=32 \end{align*} ]

Answer:

B. 32 cm