Answer:
the length of the rectangle is 19 inches.
Explanation:
Let's start by setting up equations based on the information given.
Let L be the length and W be the width of the rectangle. We know that:
L = 3W + 7 (because the length is 7 inches more than 3 times the width)
Area of rectangle = LW = 76
Now we can substitute the first equation into the second equation to get:
(3W + 7)W = 76
Simplifying, we get:
3W^2 + 7W - 76 = 0
We can solve for W by using the quadratic formula:
W = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 7, and c = -76. Plugging in these values, we get:
W = (-7 ± sqrt(7^2 - 4(3)(-76))) / 2(3)
W ≈ 4 or W ≈ -6.33
We can ignore the negative solution since the width cannot be negative. So the width of the rectangle is approximately 4 inches.
To find the length, we can use the first equation we set up:
L = 3W + 7
L = 3(4) + 7
L = 19
So the length of the rectangle is 19 inches.