Answer:
1. 5/3 cm
2. 10 in
Step-by-step explanation:
1. The length of a rectangle is 4 cm more than 3 times its width.
Let the length be L and the width B
Then,
L = 4 + 3B
If the area of the rectangle is 15 cm2
Area = LB = 15
B(4 +3B) = 15
3B² + 4B - 15 = 0
3B² - 5B + 9B - 15 = 0
B(3B - 5) + 3(3B - 5) = 0
(3B - 5)(B + 3) = 0
3B - 5 = or B + 3 = 0
B = 5/3 or -3
since B cannot be negative, B = 5/3 cm
2. The ratio of length to width in a rectangle is 2 ∶ 3.
Let the length be L and the width B
Then,
L/B = 2/3
2B = 3L, B = (3/2)L
when the area is 150 in2.
Area = LB = 150
(3/2)L² = 150
L² = 150×2÷3
L² = 100
L = √100
L = ±10
since the length cannot be negative, L = 10 in
