Question

a rectangular sheet of metal is 250 cm wide and has a diagonal of 472cm. Find the length and the area of the sheet metal.

Answer 1

Length of rectangular sheet = 400.35 cm

Area of sheet = 100087.5 cm²

Step-by-step explanation:

Given,

Width of rectangular sheet = 250 cm

Diagonal of rectangular sheet = 472 cm

Let,

x be the length of rectangular sheet.

A diagonal of rectangular, forms a right triangle where diagonal serves as hypotenuse.

Therefore;

a = x

b = 250

c = 472

Using pythagoras theorem;

$a^2+b^2=c^2\\a^2+(250)^2=(472)^2\\a^2+62500=222784\\a^2=222784-62500\\a^2=160284$

Taking square root on both sides

$\sqrt{a^2}=\sqrt{160284}\\a=400.35$

Length of rectangular sheet = 400.35 cm

Area of sheet = Length * Width

Area of sheet = 250*400.35

Area of sheet = 100087.5 cm²

Keywords: rectangle, area

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