An open top box is to be constructed by cutting out squares corners from each end of a rectangular sheet of copper, folding up the ends and then welding the ends together. find the dimensions of the box if the original length is 48 inches and width is 36 inches whose base is to have an area of 1260 square inches.

The height of the box is 3 inches

Step-by-step explanation:

A box has three perpendicular dimensions (a,b,c). Let's assume a and b are the dimensions of the base, and c is the height. The volume of the box is

And the area of the base is

The rectangular sheet of copper has dimensions 48 inches and 36 inches. We are cutting out squares corners from each end.

Set x=side of each square corner. Those corners will be folded up, leaving a base of dimensions (36-2x) and (48-2x). Its area is

According to the conditions of the question that area must be 1260 square inches, so

Operating

Rearranging

Dividing by 4

Factoring

We find two solutions

The solution x=39 is unfeasible because it will result in negative dimensions of the base of the box. We keep x=3 as the solution. The dimensions of the base are

And the height of the box is x=3

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.