Solve the problem by writing an inequality in the perimeter of a rectangular picture frame must be less than 180in. and width is 26in. what must the height of the frame be
2(26+h) < 180
you should include the steps to solve the problems please.
To solve this problem, we need to write an inequality that represents the perimeter of the rectangular picture frame.
The perimeter of a rectangle can be calculated by adding the lengths of all its sides. In this case, the rectangle has a width of 26 inches. Let's assume the height of the frame is represented by the variable 'h' (in inches).
Since a rectangle has two sides with equal length, both the top and bottom sides of the frame will have a length of 26 inches. The remaining two sides, which represent the vertical sides of the frame, will have a length of 'h' inches each.
The formula for the perimeter of a rectangle is:
P = 2w + 2h, where P represents the perimeter, w is the width, and h is the height.
Substituting the given values, we can write the inequality as:
2(26) + 2h < 180
Simplifying this inequality, we have:
52 + 2h < 180
To isolate the variable 'h', we subtract 52 from both sides of the inequality:
2h < 180 - 52
2h < 128
Finally, we divide both sides of the inequality by 2:
h < 64
Therefore, the height, represented by 'h', must be less than 64 inches for the perimeter of the rectangular picture frame to be less than 180 inches.