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The diagonal of a rectangle is 13 cm. How long is its width if it's length is 12 cm?

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Sagot :

UK2019idn

✏️RECTANGLE

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Problem: The diagonal of a rectangle is 13 cm. How long is it's width if it's length is 12 cm.

Solution: Let ABCD is an rectangle, we know that all angles of an rectangle is an right angle.

- Let take one right angled triangle, ABC in which angle B is 90 degree, and diagonal AC is 13cm and AB is 10 cm.

- We can use the Pythagorean Theorem.

  • [tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

  • [tex]AB^{2} + BC^{2} = A {c}^{2}[/tex]

  • [tex] {12}^{2} + BC^{2} = {13}^{2} [/tex]

  • [tex]144 + BC^{2} = 169[/tex]

  • [tex]BC^{2} = 169 - 144[/tex]

  • [tex]BC^{2} = 25[/tex]

  • [tex] \sqrt{ BC^{2}} = \sqrt{25} [/tex]

  • [tex]BC = 5 [/tex]

- Therefore, the width of the rectangle is:

  • [tex] \large \boxed{ \sf \green{ \: 5 cm \: }}[/tex]

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