Question

1. use the rectangle below to answer the questions that follow:

a) what is the perimeter of the rectangle?

b) if the length is increased by 4 units and width is increased by 4 units, then what is the new perimeter?

c) how did the perimeter change?

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Given $l = 12$ cm and $w=5$ cm.
$P=2(12 + 5)$

Step2: Calculate initial perimeter

$P=2\times17=34$ cm

Step3: Find new length and width

The new length is $l_{new}=12 + 4=16$ cm and the new width is $w_{new}=5 + 4 = 9$ cm.

Step4: Calculate new perimeter

Using the perimeter formula with new values, $P_{new}=2(16 + 9)=2\times25 = 50$ cm

Step5: Find perimeter change

The change in perimeter is $\Delta P=P_{new}-P=50 - 34 = 16$ cm

Answer:

a) 34 cm
b) 50 cm
c) Increased by 16 cm