Question

a scale drawing for a plot of land is shown below.
in the drawing, 4 cm represents 5 m.
assuming the backyard is rectangular, find the area of the real backyard.
area of the real backyard: 150 m²

Explanation:

Step1: Find the real - length of the backyard

Given that \(4\) cm represents \(5\) m. The length of the backyard in the drawing is \(8\) cm.
Let \(x\) be the real - length. Using the proportion \(\frac{4}{5}=\frac{8}{x}\). Cross - multiply: \(4x = 5\times8\), so \(x=\frac{5\times8}{4}=10\) m.

Step2: Find the real - width of the backyard

The width of the backyard in the drawing is \(12\) cm. Let \(y\) be the real - width. Using the proportion \(\frac{4}{5}=\frac{12}{y}\). Cross - multiply: \(4y=5\times12\), so \(y = \frac{5\times12}{4}=15\) m.

Step3: Calculate the area of the rectangular backyard

The area formula for a rectangle is \(A = length\times width\). Substitute \(length = 10\) m and \(width = 15\) m. So \(A=10\times15 = 150\) \(m^{2}\).

Answer:

\(150\) \(m^{2}\)