Question

Find the perimeter of a rectangle, whose 1 side is 12 cm & diagonal is 20 cm

Answer 1

Area =

$l \sqrt{ {d }^{2} - {l}^{2} }$

l= 12cm

d=20 cm

Area =

$12 \sqrt{ {20}^{2} - {12}^{2} } \\ 12 \sqrt{400 - 144 } \\ 12 \sqrt{256} \\ 12 \times 16 = 192 {cm}^{2}$

Answer 2

$\sf\underline{Step-by-step \: explanation}$

● To find the perimeter, breadth and length are essential out of which breadth is not given.

● As all sides of a rectangle are 90°, we can use pythagoras' theorem to find out the breadth.

● Using Pythagoras' theorem,

${hp}^{2} \: = \: {b}^{2} \: + \: {p}^{2}$

[Opposite of the perpendicular if a triangle is known as a hypotenuse]

[As we clearly see, the rectangle is forming a triangle]

${20}^{2} \: = \: {x}^{2} \: + \: {12}^{2}$

$400 \: = \: {x}^{2} \: + \: 144$

$400 \: - \: 144 \: = \: {x}^{2}$

$256 \: = \: {x}^{2}$

$\sqrt{256} \: = \: x$

● x = 16 cm

》Perimeter of a rectangle = 2(l + b)

》2(16 + 12)

》2 × 28

》 56 cm

● Hence, the perimeter is,

${\huge{\boxed{\boxed{56 \: cm}}}}$