An architect wants to do a rectangle with the diagonal of 25 inches the length of the rectangle is to be 3 inches more than triple the width. What is the dimensions she should make the rectangle
Mathematics · High School · Thu Feb 04 2021
Answered on
Given : diagonal of a rectangle = 25 inches
Let the width of rectangle be w
Then, Length of rectangle is (3w + 3) inches
We know, each angle of rectangle is of 90°.
So, by phythogoras theorem:
H² = P² + B²
(25)² = (w)² + (3w + 3)²
625 = w² + 9w² + 18w + 9 { (a+b)² = a² + 2ab +b²}
625 = 10w² + 18w + 9
10w² + 18w + 9 - 625 = 0
10w² + 18w - 616 = 0
Dividing by 2, we get
5w² + 9w - 308 = 0
Now, using middle-term split method:
5w² + 44w - 35w -308 =0
w(5w + 44) -7(5w + 44) =0
(w - 7) (5w + 44) =0
w -7 =0
w = 7
And, 5w + 44 =0
5w = -44
w = -44/5
We know, width cannot be negative. So, width is 7 inches
Now, Length = (3w + 3) inches
Length = 3(7) + 3
Length = 21 + 3
Length = 24 inches
Thus, dimensions of rectangle are 24 inches and 7 inches.