Question

a painting, including the frame, measures 52 cm by 82 cm.
a) how many centimeters of framing were needed to frame the painting?
b) how many millimeters of framing were needed to frame the painting?

Explanation:

Step1: Identify the shape and formula

The frame forms a rectangle around the painting. The length of the framing needed is the perimeter of the rectangle. The formula for the perimeter of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Substitute the values

Given $l = 82$ cm and $w = 52$ cm. Substitute into the formula: $P=2(82 + 52)$.

Step3: Calculate the perimeter in cm

First, add the values inside the parentheses: $82+52 = 134$ cm. Then multiply by 2: $P = 2\times134=268$ cm.

Step4: Convert cm to mm

Since 1 cm = 10 mm, to convert 268 cm to mm, multiply by 10. So $268\times10 = 2680$ mm.

Answer:

a) 268 cm
b) 2680 mm