Question

(a) The area of a rectangle is 300 cm and its length: breadth = 4:3. Find (i) its perimeter, and
(ii) the length of its diagonal.
The area and the perimeter of a square are A and P respectively. If the sides are doubled, the
area becomes A and the perimeter, P'. Find (i) A':A, and (ii) P':P.​

Answer 1

Answer:

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Explanation:

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Answer 2

(i). The perimeter of rectangle is 70 cm

(ii). The length of the diagonal is 25 cm

Step-by-step explanation:

Let,

The length of rectangle = 4x

The breadth of rectangle = 3x

The area of a rectangle = 300 cm²

The area of a rectangle = length × breadth

⇒ 4x × 3x = 300

⇒ 12x² = 300

⇒ x² = 300 / 12

⇒ x² = 25

⇒ x \: = \: \sqrt{25}x=

25

​

⇒ x = 5

★Value of 4x:

⇒ 4 (5)

⇒ 4 × 5

⇒ 20

★ Value of 3x:

⇒ 3 (5)

⇒ 3 × 5

⇒ 15

Therefore,

The length of rectangle = 20 cm

The breadth of rectangle = 15 cm

__________________________

(i). Find the perimeter:

Perimeter of rectangle = 2 (length +

breadth)

So,

⇒ 2 (20 + 15)

⇒ 2 (35)

⇒ 2 × 35

⇒ 70

Perimeter of rectangle is 70 cm

___________________________

(ii). Find the length of its diagonal:

By Pythagoras Theorem,

⇒ (Hypotenuse)² = (Base)² + (Height)²

⇒ (Hypotenuse)² = (20)² + (15)²

⇒ (Hypotenuse)² = 400 + 225

⇒ (Hypotenuse)² = 625

⇒ Hypotenuse = \sqrt{625}Hypotenuse=

625

​

⇒ Hypotenuse = 25

Hence,

The length of its diagonal = 25 cm

Therefore,

(i). The perimeter of rectangle is 70 cm

(ii). The length of the diagonal is 25 cm