Question

find the preimeter of a rectangale if its lenths is 15m and oneof the diagonals is 17m
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Answer 1

• The perimeter of the rectangle is 46 m

Given:

The length (l) of a rectangle is 15 m

One of the diagonal of the rectangle os 17m

To find:

The perimeter of the rectangle.

Here are the steps -

• First, we have to find the breadth(i.e. width) of the rectangle.
• Then by using the formula to find the perimeter of the rectangle we will get the required answer.

Some properties of a rectangle-

• It is quadrilateral which has equal opposite sides.
• The opposite sides are parallel to each other.
• All the interior angles of the rectangle are 90° each.
• The two diagonals are equal in length.

Now,

As each angle is 90°, so we can use the Pythagoras theorem to get the value of the breadth of the rectangle.

⇒ (Hypotenuse)² = (perpendicular)² + (base)²

⇒ (Diagonal)² = (breadth)² + (length)²

⇒ (17²) = (breadth)² + (15)²

⇒ 289 = (breadth)² + 225

⇒ 289 - 225 = (breadth)²

[By taking 225 to LHS]

⇒ 64 = (breadth)²

[By taking the square root to both the sides]

⇒ 8 = breadth

Thus,

The breadth of the rectangle is 8m

Now,

• The formula to find the breadth of a rectangle is

= 2(length + breadth) units

= 2(15 + 8)

= 2 * 23

= 46 m