A rectangle has an area of 30 Square meters and a perimeter of 34 meters. What are the dimensions of the rectangle?
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Let the length of rectangle is L
And, width of rectangle is W
Then, Area of rectangle = L × W
30 = L × W ….1
And, Perimeter = 2(L + W)
34 = 2L + 2W
Or, L + W = 17 ….2
From equation 2,
L = 17 - W
Putting value of L in equation 1, we get
(17-W) W = 30
17W - W² = 30
W² -17w + 30 = 0
By middle-term split method,
W² - 15W -2W + 30 = 0
W(W -15) - 2(W -15) = 0
(W-2) (W-15) = 0
So, W -2 = 0
W = 2
And, W -15 = 0
W = 15
Now, putting value of W in equation 1, we get
When W = 2
L × 2 = 30
L = 30/2
L = 15
When W =15
L × 15 = 30
L = 30/15
L = 2
Hence, possible dimensions of rectangle are 15×2 and 2×15