What is the length of the rectangle?
The problem of finding the length of a rectangle canbe formulated in different ways. Let's figure out how to find the lengths of the sides of a rectangle for each particular formulation. The length of the rectangle is its long side, the width of the rectangle, its short side.
- A rectangle is given. The value of its perimeter P is known, the width B of the rectangle is known. It is required to find the length of the rectangle.
The perimeter P is the sum of the lengths of all sides of the rectangle. Let L be the unknown length of the rectangle. Then P = 2B + 2L. Hence: 2L = P-2B. L = (P-2B) / 2.
- A rectangle is given. The value of its area S is known. The width of the rectangle B is known. It is required to find the length of a rectangle.
The area of the rectangle is the product of its length by width. Let L be the unknown length of the rectangle. Then S = L * B. Hence we know what the length of the rectangle is equal to: L = S / B.
- A rectangle is given. We know the value of the width of the rectangle B and the length of the diagonal A. It is required to know what the length of the rectangle is equal to.
When a rectangle is divided by a diagonal, itconsists of two rectangular triangles. For a right-angled triangle, the Pythagorean theorem is valid: "The square of the hypotenuse is equal to the sum of the squares of the legs". In this particular case, the legs are the width of the rectangle B and the length of the rectangle L. The hypotenuse is the diagonal of the rectangle. Analyzing all of the above, we get: A2= B2+ L2. Hence L2= A2- B2. L = v (A2-B2).
- A rectangle is given. The length of the diagonal of the rectangle is known. Is it known which angle? forms a diagonal with a rectangle width. Find the length of the rectangle.
The diagonal divides the rectangle into tworight triangle. Hence, the ratio of the length of the rectangle to its diagonal gives a sine of the known angle. Hence: sin α = L / A, here L is the length of the rectangle. L = sin α / A
- A rectangle is given. The length of the diagonal of the rectangle is known. Is it known which angle? forms a diagonal with a length of a rectangle. Find the length of the rectangle.
Since the diagonal, width and length of the rectangleform a rectangular triangle, then the following expression holds: cos α = L / A, i.e. The ratio of the length of the rectangle to its diagonal gives the cosine of the known angle. L = cos α / A.
We learned how to find the length of a rectangle forof all possible formulations of problems (if the perimeter and width are known, if the area and width are known, if the diagonal and angle are known, if the diagonal and width are known). Substitute known values and get a reliable answer.
