Question

a rectangle has side lengths of 4 and 75. below is the rectangle split into two small rectangles. (a) find the missing length, and then find the areas (in square units). (b) use the figure to find 4×75. 4×75=

Explanation:

Step1: Find the missing length

The total length is \(75\), and one part is \(70\). So the missing length is \(75 - 70=5\).

Step2: Calculate the area of the blue - colored rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the blue rectangle with \(l = 70\) and \(w = 4\), \(A_1=70\times4 = 280\).

Step3: Calculate the area of the red - colored rectangle

For the red rectangle with \(l = 5\) and \(w = 4\), \(A_2=5\times4=20\).

Step4: Calculate \(4\times75\)

Since \(4\times75=(70 + 5)\times4=70\times4+5\times4\), and we know \(70\times4 = 280\) and \(5\times4 = 20\), then \(4\times75=280 + 20=300\).

Answer:

(a) The missing length is \(5\). The area of the blue rectangle is \(280\) square units and the area of the red rectangle is \(20\) square units. (b) \(4\times75 = 300\)