a pair of adjacent side of a rectangle are in the ratio 3 : 4 if its diagonal is 20 cm find the length of sides and hence the perimeter of the rectangle
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given :
Length : width = 3 : 4
Let length = 3x
And, width = 4x
Diagonal = 20 cm
Since, rectangle is a right angle. So, by phythogoras theorem
(20)² = (3x)² + (4x)²
400 = 9x² + 16x²
25x² = 400
x² = 400/25
x² = 16
Taking square root of both sides, we get
x = 4
Length = 3 × 4 = 12 cm
And, width = 4×4 = 16 cm
Perimeter = 2(l + w)
= 2(12 + 16)
= 2(28)
= 56 cm
Thus, Perimeter of the rectangle is 56 cm