Question

if diagonal of rectangle is twice its width and length of diagonal is 12 cm what is area of rectangle? a = l x w

Explanation:

Step1: Find the width

Given diagonal $d = 12$ cm and $d = 2w$. So, $w=\frac{d}{2}=\frac{12}{2}=6$ cm.

Step2: Find the length

Using Pythagorean theorem $d^{2}=l^{2}+w^{2}$. Substitute $d = 12$ and $w = 6$. Then $12^{2}=l^{2}+6^{2}$, so $l^{2}=144 - 36=108$, and $l = 6\sqrt{3}$ cm.

Step3: Calculate the area

Area $A=l\times w$. Substitute $l = 6\sqrt{3}$ and $w = 6$. So $A=6\sqrt{3}\times6 = 36\sqrt{3}\text{ cm}^2$.

Answer:

$36\sqrt{3}\text{ cm}^2$