Question

the perimeter of a triangle whose one side mesure 12cm and diagonal is 20cm​

Answer 1

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

● 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,

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