A cuboid has length x cm. The width of the cuboid is 4 cm less than its length. The height of the cuboid is half of its length. The surface area of the cuboid is 90 cm^2 . Show that 2x^2 − 6x − 45 = 0
Take each side of the cuboid as an algebraic expression and multiply each by 2 to account for both sides of the shape. For example, (x)(x-4), which could be expanded to x2 -4x, and then multiplied by 2 to reach 2x2 -8x. Do the same for the other two expressions and then find the sum of all the sides together.(2)(x)(x/2) = x2. (2)(x-4)(x/2) = x2-4x. So, 2x2-8x +x2+x2-4x = 90 (90 here is the surface area of the cuboid we saw in the question). By simplifying this equation we reach 4x2-12x-90 = 0. Divide by 2, and we reach 2x2-6x-45 =0
