Maths-

General

Easy

Question

# Find the length of the diagonal and area of a Rectangle whose sides are 10 cm and 12 cm. If the perimeter of a square is 2 ( 2x+4y) , find the area ?

Hint:

### Area of a rectangle = length × breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Area of a square = side2

Perimeter of a square = 4 × side

## The correct answer is: Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively. Area of the given square is (x + 2y)2 cm2.

### step-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle

Now, sides of the rectangle = sides of the triangle (other than hypotenuse)

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ Hypotenuse2 = 122 + 102

∴ Hypotenuse2 = 144 + 100

∴ Hypotenuse2 = 244

∴ Hypotenuse = 2 √61 cm .............................. (Taking square root both the sides)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 12 × 10 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 120 cm2

Perimeter of the given square = 4 × sides

∴ 2 (2x + 4y) = 4 × sides

∴ 4x + 8y = 4 × sides

∴ x + 2y = side .................. (Dividing both sides by 4) ................................ (Equation i)

Now, Area of the given square = side2

∴ Area of the given square = (x + 2y)2 ......................................................................................... (From Equation i)

Final Answer:-

∴ Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively.

Area of the given square is (x + 2y)2 cm2.

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