Question

find the value of x so that the two rectangles have the same area. first rectangle: height 7 cm, base segments x cm and 3 cm; second rectangle: base 6 cm, height segments x cm and 5 cm x = \square

Explanation:

Step1: Find area of first rectangle

Length of first rectangle: \(x + 3\) cm, Width: \(7\) cm. Area \(A_1 = 7(x + 3)\)

Step2: Find area of second rectangle

Length of second rectangle: \(6\) cm, Width: \(x + 5\) cm. Area \(A_2 = 6(x + 5)\)

Step3: Set areas equal and solve for x

\(7(x + 3) = 6(x + 5)\)
Expand: \(7x + 21 = 6x + 30\)
Subtract \(6x\) and \(21\): \(7x - 6x = 30 - 21\)
Simplify: \(x = 9\)

Answer:

\(9\)