Answer:
Width = 6.45 cm
Length = 8.6 cm
Explanation:
the sides of a rectangle are such that the width is three-quarters of the length. if the diagonal is 15cm find the length and the width.
From the question,
W = 3/4L
W = 3L/4
When given diagonal,
W² + L² = D²
Where, D = Diagonal
W = Width
L = Length
Hence, Substituting 3L/4 for W
(3L/4)² + L² = 15²
9L²/16 + L² = 225
L²(9/16 + 1) = 225
Divide both side by 9/16 + 1
L² = 225/(9/16 + 1)
Square root both side
L = √225/(9/16 + 1)
L = 15/3/4 + 1
L = 15 ÷ 1 3/4
L = 15 ÷ 7/4
L = 15 × 4/7
L = 8.6cm
W = 3L/4
W = 3(8.6)/4
W = 6.45cm