Question

In Figure 1, ABCD is a rectangle with AB = 12 cm and BC= 7 cm. AK= BL= CM= DN = x cm. If the area of KLMN is 54 cm², find x.

Answer 1

2(1/2)x(7 - x) + 2(1/2)x(12 - x) + 54 = 84

7x - x² + 12x - x² = 30

-2x² + 19x - 30 = 0

2x² - 19x + 30 = 0

(2x - 15)(x - 2) = 0

x = 2