Answer:
Length = 7cm
Width = 4cm
Step-by-step explanation:
The area of a rectangle is calculated as:
Length × Width
The length of a rectangle is 13 centimeters less than five times its width.
This is expressed Mathematically as:
L = 5W - 13
Its area is 28 square centimeters.
Therefore:
28cm² = 5W - 13 × W
28 = (5W - 13)W
28 = 5W² - 13W
Hence,
5W² - 13W - 28 = 0
We factorise
5W² - 20W - 7W - 28 = 0
5W(W - 4) + 7(W - 4) = 0
(5W + 7)(W - 4) = 0
5W + 7 = 0
5W = -7
W = -7/5
W - 4 = 0
W = 4 cm
Solving for the length
L = 5W - 13
L = 5 × 4 cm - 13
L = 20 cm - 13 cm
L = 7 cm
Therefore, the dimensions of the rectangle is:
Length = 7cm
Width = 4cm