Question

The area of a rectangle is 21 cm², if one side exceeds the other by 4 cm ,find the dimensions of the rectangle.​

Answer 1

Answer:

7cm

Explanation

Let Length of one side of given rectangle = x cm; then

Length of second side of given rectangle = x + 4 cm

Formula for Area of rectangle = L X W

Put values in formula , we have

x . ( x + 4) = 21

=> x^2 + 4x = 21

=> x^2 + 4x - 21 = 0

=> x^2 + 7x - 3x - 21 = 0

=> x(x + 7) -3(x + 7) = 0

=> (x -3) (x + 7) = 0

=> x -3 = 0 or x + 7 = 0

=> x = 3 or x = - 7

Length always have positive value.

Therefore, Length of one side (dimension) of given rectangle = x = 3 cm; then

Length of second side (dimension) of given rectangle = x + 4 = 3 + 4 = 7 cm Answer

Check:

Formula for Area of rectangle = L X W

Put values of sides

Area of rectangle = 3 X 7

Area of rectangle = 21 square cm .. Proved

Answer 2

Given:-

• Area of Rectangle = 21cm²

To Find:-

• The dimensions of the rectangle.

Solution:-

Let's

Length of Rectangle be x & breadth be (x+4).

$\boxed{\sf{Area\;of\; Rectangle = Length×Breadth}}$

$(x)(x + 4) = 21 \\ {x}^{2} + 4x - 21 = 0 \\ {x}^{2} + 7x - 3x - 21 = 0 \\ x(x + 7) - 1(x + 7) = 0 \\ (x - 1)(x + 7) = 0 \\ x = 1(or) - 7$

Here, x = -7

Length = -7

Breadth = -7+4 = -3

• Length ☞ $\Large{\red{\bold{7}}}$
• Breadth ☞ $\Large{\green{\bold{3}}}$

$\Large{✓}$

Hope It Helps You ✌️