Question

Find the perimeter of a rectangle with the diagonal 13 cm and length of one side is 12cm
a .33
b.34
c.35
d.36
​

Answer 1

$P=34cm$

Length = 12cm

Diagonal = 13cm

P=2(l+w)

d=w ^{2} 2+l2^{2}

$Solving \: for \: P$

$P=2l+2d^{2} ﹣l ^{2} =2·12+2·132﹣122=34cm$

Answer 2

WE NEED TO USE PYTHOGORAS THEOREM

We know diagnol = Hypotenuse

Hypotenuse² = side² + side²

13² = 12² + side²

169 = 144 + side²

side² = 169 - 144

side² = 25

side = √25

side = 5cm

We have lenght and breadth now.

Lenght = 12 cm

Breadth = 5cm

Perimeter of rectangle = 2*(L+B)

                                       = 2*(12 cm + 5cm)

                                       = 2*(17 cm)

                                       = 34 cm

∴ The perimeter of rectangle is 34 cm