Question

find the perimeter of a rectangle which diagonal is 17 cm and length is 15cm
please give me with the formula

Answer 1

Answer:

if we consider one of the diagonals of the rectangle, we can see that two right triangles are formed ( right triangle because angles of a rectangle are 90°) in which length of the rectangle is acting like a base of the triangle and breadth of the rectangle is acting like a height of the triangle and diagonal of the rectangle is acting like a hypotenuse of the triangle .

So, we can apply pythagoras theorem to find out the unknown breadth .

Pythagoras theorem states that in a right triangle--

Hypotenuse²= Height ²+ Base²

So, we can compare hypotenuse , base and height of the triangle with length, breadth and diagonal as mentioned before. So, the formula becomes--

diagonal ²= length ²+breadth ²

Diagonal = 17cm

length = 15 cm

∴ 17²= 15²+ breadth²

or, 289= 225+ breadth²

or, 289-225= breadth²

∴ breadth = √(289-225)

= √64

= 8

Perimeter = 2( length + breadth )

= 2( 8 + 15)

= 2×23

= 46 ( ANSWER)

Hope everything is clear to you.