i need help with this math question

Question

A rectangular animal enclosure is 10m by 15m. the enclosure is to be made larger by increasing each side length by the same amount. if the area of the new enclosure is to be double the are of the current enclosure, find the dimensions of the new enclosure. and INCLUDE A DIAGRAM!

Answer 1

Area = 10 times 15 = 150

double 150 = 300 m^2

(10+x)(15+x) = 300

x^2 + 25x + 150 = 300

x^2 + 25 -150 = 0

(x+30)(x-5) = 0

x = 5 or -30 (ignore the negative solution)

increase 10 by 5 to get 15 meters wide

increase 15 by 5 to get 20 meters long

15 times 20 = 300 square meters = double the original area

Answer 2

Hello, please take a look at the work below:

Original Enclosure: Length is 15, Width is 10. So, the Area is length x width, giving you 15 m x 10 m = 150 m^2.

What would be your new area for the larger enclosure? Well, 150 x 2 = 300 (do this because you want to double the enclosure's area.

Okay, so we have established that the new area needs to be 300 m^s. Now let's look at the new length and width.

Let us set x as the amount that both the length and width are increased by (since they are increased by the same amount, x works for both).

So we have:

Length = (x+15) <---------- 15 for the original length, added to x (to be determined)

Width = (x+10) <----------- 10 for the original width, added to x (to to determined)

So, New Area = New Length x New Width

300 = (x+15)(x+10)

300 = x^2 +10x +15x +150 <------------- FOIL

300 = x^2 +25x +150

0 = x^2 +25x - 150 <-------------- subtract 300 from each side

0 = (x + 30) (x - 5) <-------------- Factor

Set x+30 = 0 and x-5 = 0

x = -30 or x = 5..... can length be negative? No. So -30 is not possible. We must choose x=5.

New length: 5 + 15 = 20 m

New width: 5+ 10 = 15 m

Check: 15 x 20 = 300 and we are good to go!

As for the diagrams, you should draw a rectangle with length as 15 and width 10, and then a new one with length = (x+15) and width = (x+10)