Finding the volume

Question

The area of the rectangle is 56cm². The rectangle is the base of a right prism. Find the volume of right prism if the height of the prism is x-2 cm. One long side of the rectangle is x+2 and a short side is x+3.

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the Volume of a Triangular Prism with given Area of 56 square centimetres, a height of (x-2), a length of (x+2) and a width of (x+3). First, we use the equation of the area of a rectangle such that

l*w = A

(x+2)(x+3) = 56.......Then we begin solving for x such that

x²+5x+6 = 56

x²+5x-50 = 0

(x+10)(x-5) = 0

x = -10, 5

We cannot use x = -10 because we cannot have a negative length, width or height. So we use x = 5 such that

length = (x+2) = 7 centimetres

width = (x+3) = 8 centimetres

height = (x-2) = 3 centimetres

Then, we apply the Volume of a Triangular Prism such that V = (1/2)(b)(h)(l) to obtain

V = (1/2)(7)(8)(3)

V = (1/2)(168)

V = 84 cubic centimetres

I hope this helped!