Question

the figure shown has a total area of 420 m². which equation can be used to find the value of x? 420 = 25·15 + 3x·x 420 = 25·x + 15·2x 420 = 25·x + 15·3x 420 = 25·4x + 15·3x

Explanation:

Step1: Divide the figure into two rectangles

The left - hand rectangle has dimensions \(25\) m (height) and \(x\) m (width). The area of a rectangle is \(A = \text{length}\times\text{width}\), so its area \(A_1=25\times x\).
The right - hand rectangle has height \(15\) m. The width of the right - hand rectangle: The total height of the figure is \(25\) m. If the height of the left - hand part (above the right - hand rectangle) is \(x\) m, then the height of the part above the right - hand rectangle is \(25 - 15\) m. Since the figure is composed of two rectangles, and by observing the structure, the width of the right - hand rectangle (parallel to the \(3x\) side) can be found. The width of the right - hand rectangle is \(2x\) m (because if we consider the non - overlapping parts, \(25=x+(25 - 15)\) and by analyzing the side lengths in terms of \(x\), using the relationship between the sides of the L - shaped figure). The area of the right - hand rectangle \(A_2 = 15\times2x\).

Step2: Use the total area formula

The total area \(A=A_1 + A_2\). Given \(A = 420\space m^{2}\), we substitute \(A_1\) and \(A_2\) into the formula: \(420=25\times x+15\times2x\).

Answer:

\(420 = 25\cdot x+15\cdot2x\)