Question

The length of a rectangle is three times of its width. If the length of the diagonal is
$\sqrt[8]{10} metres$
then the perimeters of rectangle is

​

Answer 1

Answer:

Perimeter = 64 m

Step-by-step explanation:

Let the Breadth be x,

So, Length = 3x

we are given Diagonal = 8√10 m

We also know that,

Each angle in a rectangle is 90° and forms a right triangle when a diagonal is drawn.

Thus,

By Pythagoras theorem,

Length² + Breadth² = Diangonal²

(3x)² + x² = (8√10)²

3²x² + x² = 8²(√10)²

9x² + x² = 64 × 10

10x² = 640

x² = 640/10

x² = 64

x = √64

x = 8 m

We are not considering the-ve value because it is a rectangle, and its sides can't be negative.

So,

Length = 3 × 8

Length = 24 m

Breadth = 8 m

Now,

Perimeter of a rectangle = 2(L + B)

P = 2(24 + 8)

P = 2 × 32

P = 64 m

Hence, the Perimeter is 64 m

Hope it helped and believing you understood it........All the best.