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2 years ago

Which iequailty model and solution set best represents the possible side lengths of miriam's bulletin board?

Mathematics

1 answer:

faltersainse [42]2 years ago

6 0

Question:

Miriam is making a bulletin board that is shaped like a square. She has 72 inches of border material. If x represents the length of one side of the bulletin board, which inequality model and solution set best represents the possible side lengths of Miriam's bulletin board?

Answer:

$x \le 18$

Step-by-step explanation:

Given

$Border\ Material = 72$

Required

Determine an inequality for x

Represent the side lengths of the border with y. So:

Since the border is on the 4 sides, then

$4y = 72$ -- i.e. the perimeter of the border material

Solve for y

$y =\frac{72}{4}$

$y =18$

Recall that x represents the board's side length.

Since x will be situated inside the boarder, then.

$x \le y$

Substitute $y =18$

$x \le 18$

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Step-by-step explanation:

The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;

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Please note that the names ( $opposite$ ) and ( $adjacent$ ) are subjective and change depending on the angle one uses in the ratio. However the name ( $hypotenuse$ ) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.

In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ( $tan$ ) ratio.