Solve the problem by writing an inequality.
If the perimeter of a rectangular picture frame must be less than 160 in., and the width is 25 in., what must the height h of the frame be?
HINT: "must be less than" does not have an equal
The formula for calculating the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this problem, the width is given as 25 inches and the perimeter must be less than 160 inches.
We can write the inequality as:
2(l + 25) < 160
Simplifying the inequality, we have:
l + 25 < 80
Now, isolate the variable l by subtracting 25 from both sides:
l < 80 - 25
l < 55
Therefore, the height h of the frame must be less than 55 inches.
To solve this problem by writing an inequality, we know that the perimeter of a rectangular picture frame is given by the formula P = 2w + 2h, where P is the perimeter, w is the width, and h is the height. We are given that the width is 25 inches, and the perimeter must be less than 160 inches.
So, we can write the inequality as:
2w + 2h < 160
Substituting the value of w as 25, we have:
2(25) + 2h < 160
Simplifying further:
50 + 2h < 160
Subtracting 50 from both sides:
2h < 160 - 50
2h < 110
Finally, dividing both sides by 2:
h < 55
Therefore, the height of the frame must be less than 55 inches.
To write an inequality and solve this problem, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
In this case, the width is given as 25 inches. Let's assume the length of the picture frame is h inches.
The perimeter of the picture frame must be less than 160 inches. So, we can write the inequality:
2(h + 25) < 160
Now, let's solve the inequality for h:
2h + 50 < 160
Subtract 50 from both sides of the inequality:
2h < 110
Finally, divide both sides of the inequality by 2:
h < 55
Therefore, the height (h) of the picture frame must be less than 55 inches for the perimeter to be less than 160 inches.