Question

Find the perimeter of a rectangle if one of its sides is 24cm and a diagonal is 25cm. step by step
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Answer 1

Step-by-step explanation:

Data:

• l = 24cm
• b = ?
• diagonal = 25cm

Solution:

using Pythagoras theorem,

$\implies$ $\sf{ 25^2 = 24^2 + b^2}$

$\implies$ $\sf{ b^2= 25^2 - 24^2}$

$\implies$ $\sf{b^2 = 625-576 }$

$\implies$ $\sf{b^2=49 }$

$\implies$ $\sf{ b= \sqrt{49}}$

$\therefore$ $\sf{b = 7 }$

To find perimeter:

$\implies$ $\sf{ P= 2(l+b)}$

$\implies$ $\sf{ 2(24+7)}$

$\implies$ $\sf{2(31) }$

$\therefore$ Perimeter = $\boxed{\sf{ 62\ cm}}$

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