Question

A rope is √250 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 3:2 . What is the length of the longer piece expressed in simplest radical form?

Answer 1

Answer:

Length of longer piece is 15√10 units

Step-by-step explanation:

Firstly we will write √250 in the simplest radical form. i.e.

√250 = 5√10

Now we have a rope of length 5√10 and we have to divide it in ratio 3:2.

Let 3x be the length of the longer piece

and 2x be the length of the smaller piece.

So, the total length of rope is 5x.

Hence, we can write length of longer piece = $\dfrac{3x \times 5\sqrt{10}}{5x}$

⇒ Length of longer piece = 3 × 5√10

⇒ Length of longer piece = 15√10 units

Answer 2

what we do is, simply split the whole amount by the sum of the ratios and distribute accordingly, so in this case we'll split up √250 by (3+2) and distribute to each ratio, let's do so

$\bf \cfrac{\textit{longer piece}}{\textit{shorter piece}}\qquad 3:2\qquad \cfrac{3}{2}\qquad \qquad \cfrac{3\cdot \frac{\sqrt{250}}{3+2}}{2\cdot \frac{\sqrt{250}}{3+2}}\qquad \begin{cases} 250=&5\cdot 5\cdot 10\\ &5^2\cdot 10 \end{cases} \\\\\\ \cfrac{3\cdot \frac{\sqrt{5^2\cdot 10}}{5}}{2\cdot \frac{\sqrt{5^2\cdot 10}}{5}}\implies \cfrac{3\cdot \frac{5\sqrt{10}}{5}}{2\cdot \frac{5\sqrt{10}}{5}}\implies \cfrac{3\sqrt{10}}{2\sqrt{10}}~\hfill \stackrel{\textit{longer piece}}{3\sqrt{10}}$