Question

Someone please solve with work. Much appreciated!! A rectangular sheet of metal is 250 cm wide and has a diagonal of 472cm. Find the length of the sheet of the metal and the area.

Answer 1

The length of rectangular sheet is 400.35 cm

The area of rectangular sheet is 100087.5 square centimeters

Solution:

Given that,

Width of rectangular sheet = 250 cm

Diagonal of rectangular sheet = 472 cm

To find: length and area of rectangular sheet

The figure is attached below

Consider the rectangle ABCD

CD is the length = ?

BC is the width = 250 cm

BD is the diagonal = 472 cm

The diagonal BD and length and width forms a right angled triangle with diagonal as hypotenuse

We can use Pythogoras theorem to find length

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition for right angled triangle DCB,

$BD^2=BC^2 + CD^2$

$472^2 = 250^2 + CD^2\\\\222784 = 62500 + CD^2\\\\CD^2 = 222784 - 62500\\\\CD^2 = 160284\\\\\text{Take square root on both sides }\\\\CD = \sqrt{160284}\\\\CD = 400.35$

Thus length of rectangular sheet is 400.35 cm

Area of rectangle = length x width

$area = 400.35 \times 250 = 100087.5$

Thus area of rectangular sheet is 100087.5 square centimeters