Question

The perimeter of a rectangle is 46m and his diagonal is 17m. then find the area of rectangle ​

Answer 1

Answer:

• Area of rectangle = 120 m².

Step-by-step explanation:

Let l and b be the length and breadth of the rectangle.

Given:

• Perimeter of rectangle = 46 m
• Diagonal = 17 m

To Find:

• Area.

So, according to question

⇒ Perimeter = 2 (l + b)

⇒ 46 = 2 (l + b)

⇒ l + b = 23    

⇒ b = 23 - l       .............(1)

Now, in the triangle formed by the adjacent sides and one diagonal of the rectangle, using Pythagoras theorem.

⇒ l² + b² = diagonal²

⇒ l² + b² = 17²

Now, put the value of b from equation (1), we get

⇒ l² + (23 - l)² = 289

⇒ l² + 529 + l² - 46l = 289

⇒ 2l² - 46l + 240 = 0

Now, take 2 common, we get

⇒ l² + 23l + 120 = 0

⇒ l² - 15l - 8l + 120 = 0

⇒ l(l - 15) - 8(l - 15) = 0

⇒ (1 - 8)(1 - 15) = 0

⇒ l = 8 m or 15 m.

Now, from 1st equation,

⇒ b = 23 - l

If l = 8 m, then

⇒ b = 23 - 8

⇒ b = 15 m

If l = 15 m, then

⇒ b = 23 - 15

⇒ b = 8 m

Now, area of rectangle = l × b

⇒ Area of rectangle = 8 × 15

⇒ Area of rectangle = 120 m²

Hence, area of rectangle = 120 m².

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