Explanation
Length of rectangle $$ (l) $$ is 24 cm.
Length of diagonal $$ (d) $$ is 30 cm.
Let the length of breadth be $$ b $$.
Write the formula to calculate the diagonal of rectangle.
$$ d=\sqrt{b^{2}+h^{2}} $$ (1)
Substitute the values in equation (1).
$$ 30 = \sqrt{b^{2}+\left ( 24 \right )^{2}} $$
Solve for $$ b $$.
$$ b^{2}=900-576 $$
$$ b^{2}=324 $$
$$ b=\pm 18 $$
Since the breath cannot be negative. So, neglect the negative value of breadth. Hence, the breadth of the rectangle is $$ 18 $$ cm.
Write the formula to calculate perimeter of rectangle.
$$ P=2\left ( l+b \right ) $$ (2)
Substitute the values in equation (2).
$$ P=2\left ( 24+18 \right ) $$
$$ =2\left ( 42 \right ) $$
$$ =84 $$
Thus, the perimeter of rectangle is $$ 84 $$ cm.
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