Question

A rectangular restaurant kitchen has a perimeter of 34 meters and an area of 70 square meters. What are the dimensions of the kitchen?

Answer 1

7 metres by 10 metres

Explanation:

let's call the length L and the width W

rectangular, so 2L + 2W = perimeter = 34

area = LW = 70, L = 70/W.

now input this into the equation of perimeter to find W:

2L + 2W = 34

2(70/W) + 2W = 34

140/W + 2W = 34

multiply through by W to get

(140/W) W + 2W (W) = 34W

140 + 2W² = 34W

bring the 34W to the left side

2W² - 34W + 140 = 0

divide all by 2

W² - 17W + 70 = 0

two numbers that add up to -17 while multiplying together to give +70 are

- 10 and -7

so we have (W - 7) (W - 10) = 0

W = 7 or 10

L also equals 7 (when W = 10) or L equals 10 (when W = 7)

Answer 2

Answer: 7 by 10 (7 meters wide 10 meters long)

Explanation:

7+7+10+10=34 for the perimeter and 7x10=70 for the area, therefore 7 meters wide 10 meters long is the answer.