Question

a square and a rectangle have the same perimeter of 40 meters. if the squares side length is 10 meters, what is the area of the rectangle if its length is 14 meters? a 72 m² b 24 m² c 84 m² d 32 m²

Explanation:

Step1: Find the width of the rectangle

The perimeter formula for a rectangle is \(P = 2\times(l + w)\). Given \(P = 40\) meters and \(l=14\) meters.
Substitute into the formula: \(40=2\times(14 + w)\)
Divide both sides by 2: \(20 = 14+w\)
Subtract 14 from both sides: \(w=20 - 14=6\) meters.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A=l\times w\). Substitute \(l = 14\) meters and \(w = 6\) meters.
\(A=14\times6 = 84\) \(m^{2}\)

Answer:

C. \(84\ m^{2}\)