One side of the rectangle is 4 larger than the other. Find the sides of a rectangle if its area is 96.

The task
The length of the rectangle is a -?, 4 more than b
Width of rectangle b -?
Area of a rectangle S – 96
Solution
1. Let’s compose two equations based on the condition
a = b + 4
a b = 96
2. Substitute the value a into the second equation and find b
(b + 4) b = 96
b ^ 2 + 4 b – 96 = 0
D = 4 4 – 4 1 (-96) = 16 + 384 = 400
b1 = (-4 + v400) / 2 1 = (-4 + 20) / 2 = 8 – the width of the rectangle
b2 = (-4 – v400) / 2 1 = – 24/2 = -12 <0
3. Calculate the length of the rectangle a
a = b + 4 = 8 + 4 = 12
4. Verification
S = a b = 12 8 = 96
a – b = 12 – 8 = 4
Answer: length a – 12, width b – 8.