Question

A rectangle has a length of X +5 and a width of X -5 and has an area of 15 square units find the length and width of the rectangle.

Answer 1

Answer:L=11.3

W=1.3

Step-by-step explanation:

Answer 2

Given :-

• Length of rectangle = x + 5
• width of rectangle = x - 5
• Area of rectangle = 15 unit²

To find:-

• Actual length and width of rectangle

Solution:-

So to find actual length and width of rectangle, we need to find value of x.

we know:-

$\bigstar \boxed{ \rm Area~of \: rectangle = length \times width}$

So:-

$\hookrightarrow \sf Area~of \: rectangle = length \times width$

$\hookrightarrow \sf 15=(x + 5)(x - 5)$

$\hookrightarrow \sf 15=x (x - 5) +5(x - 5)$

$\hookrightarrow \sf 15=x^2 - 5x +5(x - 5)$

$\hookrightarrow \sf 15=x^2 - 5x +5x - 25$

$\hookrightarrow \sf 15=x^2 - \cancel {5x} +\cancel {5x} - 25$

$\hookrightarrow \sf 15=x^2 -0 - 25$

$\hookrightarrow \sf 15=x^2 - 25$

$\hookrightarrow \sf 15 + 25=x^2$

$\hookrightarrow \sf 15 + 25=x^2$

$\hookrightarrow \sf 40=x^2$

$\hookrightarrow \sf x^2 = 40$

$\hookrightarrow \sf x = \sqrt{40}$

$\hookrightarrow \sf x = \sqrt{2 \times 2 \times 10}$

$\hookrightarrow \sf x = 2 \sqrt{10}$

$\hookrightarrow \sf x = 2 \times 3.16$

$\hookrightarrow \sf x = 2 \times 3.16$

$\hookrightarrow \bf x = 6.32(approx)$

• Length = x + 5
• Length = 6.32 + 5
• Length = 11.32 (units)

• Breadth = x - 5
• Breadth = 6.32 - 5
• Breadth = 1.32 (units)