Question

The length of a rectangle is 3 centimeters less than five times its width. Its area is 14 square centimeters. Find the dimensions of the rectangle. W= L=​

Answer 1

Step-by-step explanation:

Let breadth =x

Length=5x-3

As we know that in a rectangle

$\boxed{\sf Area=lb}$

• Substitute the values

${:}\hookrightarrow\sf x (5x-3)=14$

${:}\hookrightarrow\sf 5x^2-3x=14$

${:}\hookrightarrow\sf 5x^2-3x-14=0$

${:}\hookrightarrow\sf 5x^2-10x+7x-14=0$

${:}\hookrightarrow\sf 5x (x-2)+7 (x-2)=0$

${:}\hookrightarrow\sf (x-2)(5x+7)=0$

${:}\hookrightarrow\sf x-2=0\quad or\quad 5x+7=0$

${:}\hookrightarrow\sf x=2\:or\:x=\dfrac {-7}{5}$

• Ignore negative value

${:}\hookrightarrow\sf Breadth =2cm$

${:}\hookrightarrow\sf Length=5 (2)-3=10-3=7cm$