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Sagot :

Devishri1977idn

Answer:

Step-by-step explanation:

To find the breadth use Pythagorean theorem

Breadth² = diagonal² - length²

               = 34² - 30²

               = 1156 - 900

               = 256

Breadth = √256 = 16 cm

Breadth = 16 cm

Perimeter = 2*(length + breadth) = 2*(30 + 16) = 2*46 = 92 cm

Area = length * breadth = 30 *16 = 480 cm²

S O L U T I O N:

Let's assume that the given rectangle be ABCD and in that let ∆ABC be the right angled triangle formed from it.

Now we've been asked to find out the breadth. By applying Pythagoras theorem here in our rectangle ABCD we have,

  • length (l) = 30cm

  • diagonal (d) = 34cm

  • breadth (b) = ?

[tex]:\implies\tt{ {b}^{2} = {d}^{2} - {l}^{2} }[/tex]

[tex]:\implies\tt{ {b}^{2} = {34}^{2} - {30}^{2} }[/tex]

[tex]:\implies\tt{ {b}^{2} = 1156 - 900}[/tex]

[tex]:\implies\tt{ {b}^{2} = 256}[/tex]

[tex]:\implies\tt{b = \sqrt{256} }[/tex]

[tex]:\implies\tt{b = 16}[/tex]

For the formula of area (a) = ? it is given by,

[tex]:\implies\tt{a = l \times b}[/tex]

[tex]:\implies\tt{a = 30 \times 16}[/tex]

[tex]:\implies\tt{a = 480 {cm}^{2} }[/tex]

For the formula of perimeter (p) = ? is given by,

[tex]:\implies\tt{p = 2 \times (l + b)}[/tex]

[tex]:\implies\tt{p = 2 \times (30 + 16)}[/tex]

[tex]:\implies\tt{p = 2 \times 46}[/tex]

[tex]:\implies\tt{p = 92cm}[/tex]

  • The breadth, area and perimeter of rectangle is 16, 480cm² and 92cm.
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