algebraic question

Question

a rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. what is the rectangles width and length

Answer 1

Hi Jason,

You were given that the length, L =(5x+2) and the width, W=(2x+1) and the area of a rectangle is LxW=100. So we calculate the area in terms of x by multiplying LxW

LxW=(5x+2)(2x-1)=10x²-x-2 and this is equal to the area which you were told is 100 sqft:

so the equation for determining x becomes:

10x²-x-102=0 which is a quadratic equation, the solution (roots) are -3.1441 and 3.2441 approx.

The negative root gives a L and W the has no physical meaning. Using the positive root gives

L=5.4882 ft. and W= 18.2205 ft.

Hope this helps.....

Jim

Answer 2

(5x + 2)(2x - 1) = 100

Can you solve for x and answer?