Question

the area of a rectangle is 30 to the square root of 3750 square inches, and the length is 3 to the square root of 250 inches. what is the width of the rectangle?

Answer 1

Answer:

• $\sf { width =10 \sqrt{15} \:inches}$

Solution:

We are given that:

• Area of rectangle is 30√3570
• Length of the rectangle is 3√250

Area of rectangle is given by:

$\implies\quad{\pmb{ \sf{Area = length\times width}} }$

Hence, putting the values in the formula:

$\implies\quad \sf{ A = l\times w}$

$\implies\quad \sf{ 30\sqrt{3750}=3\sqrt{250}\times w}$

$\implies\quad \sf{3\sqrt{250}\times w = 30\sqrt{3750} }$

$\implies\quad \sf{ w =\dfrac{30\sqrt{3750}}{3\sqrt{250}}}$

$\implies\quad \sf{ w =10\dfrac{\sqrt{3750}}{\sqrt{250}}}$

$\implies\quad \sf{ w = 10\times\sqrt{\dfrac{3750}{250}}}$

$\implies\quad \underline{\underline{\pmb{\sf{ w =10\sqrt{15}}}}}$