The area of a rectangular garden is 112 square meters. The width is 10 meters longer than ​one-half of the length. Find the length and the width of the garden. Use the​ formula, arealengthwidth.

Answer 1

Hello, thank you for taking the time to post your question!

the underlying formula we want to use here is that area = length x width, so for this one that would mean

112 = l x w for one of the equations

Then the other equation is based on the idea that the width is 10 meters longer than one-half of the length. That means

w = 1/2l + 10

If you substitute that back into the original equation you get

112 = l (1/2l + 10)

112 = 1/2l^2 + 10l

Then if you solve that quadratic for the value of l you will be able to plug it back into the width equation to find the width

When I do that here I end up getting length = 8 meters and width = 14 meters

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let L be length and W be width

W = 0.5L +10

Area = L x W = 112

L x (0.5L + 10) = 112

0.5L² + 10L =112

L² + 20 L = 224

L² + 2(10) L + 100 = 224 +100

(L + 10)² =324

L+10 = _-⁺ (324)^0.5

L = -10 + 18 = 8

OR

L = -10 - 18 = -28 (reject due to <0)

L = 8

W = 0.5 (8) + 10 = 14

Answer check: L x W = 8 x 14 = 112

Note: strictly speaking, the "Length" should generally be the longer than the width, so there may be some issues with the problem's wording, as the "Width" is longer than the "Length" in the solution.

Answer 3

w = 10 + L/2

112 = Area = wL

= (10+L/2)L

= 10L + L^2/2 = 112

L^2 + 20L = 224

L^2 +20L +100 = 224+100

(L+10)^2 = 324

L+10 = sqr324

L = sqr324-10 = 18-10 = 8 m = Length

w = 112/8 = 14 m = width

garden is 8 meters by 14 meters

8x14 = 112 m^2

w =10+L/2 = 10+8/2 = 10+4= 14 m