SOLUTION: I am having a lot of trouble with this question: "The area of a rectangle is 528 sq mm. The base is 8 more than three times the height. What is the perimeter?" I started the proble

Algebra ->  Rectangles -> SOLUTION: I am having a lot of trouble with this question: "The area of a rectangle is 528 sq mm. The base is 8 more than three times the height. What is the perimeter?" I started the proble      Log On


   

Question 333636: I am having a lot of trouble with this question: "The area of a rectangle is 528 sq mm. The base is 8 more than three times the height. What is the perimeter?" I started the problem by setting up this equation: 528=h(3h+8) where h=height. Then I got 528=3h^2+8h. However, I'm not sure what to do after this.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
528=3h%5E2%2B8h Start with the given equation.


0=3h%5E2%2B8h-528 Subtract 528 from both sides.


Notice that the quadratic 3h%5E2%2B8h-528 is in the form of Ah%5E2%2BBh%2BC where A=3, B=8, and C=-528


Let's use the quadratic formula to solve for "h":


h+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


h+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%283%29%28-528%29+%29%29%2F%282%283%29%29 Plug in A=3, B=8, and C=-528


h+=+%28-8+%2B-+sqrt%28+64-4%283%29%28-528%29+%29%29%2F%282%283%29%29 Square 8 to get 64.


h+=+%28-8+%2B-+sqrt%28+64--6336+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-528%29 to get -6336


h+=+%28-8+%2B-+sqrt%28+64%2B6336+%29%29%2F%282%283%29%29 Rewrite sqrt%2864--6336%29 as sqrt%2864%2B6336%29


h+=+%28-8+%2B-+sqrt%28+6400+%29%29%2F%282%283%29%29 Add 64 to 6336 to get 6400


h+=+%28-8+%2B-+sqrt%28+6400+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


h+=+%28-8+%2B-+80%29%2F%286%29 Take the square root of 6400 to get 80.


h+=+%28-8+%2B+80%29%2F%286%29 or h+=+%28-8+-+80%29%2F%286%29 Break up the expression.


h+=+%2872%29%2F%286%29 or h+=++%28-88%29%2F%286%29 Combine like terms.


h+=+12 or h+=+-44%2F3 Simplify.


So the solutions are h+=+12 or h+=+-44%2F3

However, a negative height doesn't make any sense. So we'll ignore h+=+-44%2F3


This means that the height is 12 mm.


I'll let you use this info to find the perimeter.