Question

The perimeter of the rectangle whose length is $24cm$ and the diagonal is $30cm$ is:

• A. $84cm$
• B. $42cm$
• C. $54cm$
• D. $108cm$

Answer 1

The correct option is A $84cm$

Length of rectangle $\left(l\right)$ is 24 cm.

Length of diagonal $\left(d\right)$ 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.

$P=2(l+b)$ (2)

Substitute the values in equation (2).

$P=2(24+18)$

$=2\left(42\right)$

$=84$

Thus, the perimeter of rectangle is $84$ cm.