Question

A rope is sq rt. 250 units long. If cut into 2 pieces so that the lengths of the pieces are in the ratio of 3:2, what is the length of longer piece in simplest radical form?

Answer 1

The length piece in simplest radical form is $\boxed{3\sqrt {10} }{\text{ or }}\boxed{9.48}.$

Further explanation:

Given:

The length of the rope is $\sqrt {250}.$

The rope is cut into 2 pieces.

The lengths of the pieces are in the ratio of $3:2.$

Explanation:

The ratio of the cut pieces is 3:2.

Let the larger length of the rope as $3x$ and the smaller length of the rope as $2x.$

The total length of the pieces is $\sqrt {250}$.

$\begin{aligned}3x + 2x &= \sqrt {250}\\5x &= 5\sqrt {10}\\x&=\frac{{5\sqrt {10} }}{5}\\x&= \sqrt {10}\\\end{aligned}$

The length of smaller piece is $2x = 2\sqrt {10}.$

The length of larger piece is $3x = 3\sqrt {10}.$

The length piece in simplest radical form is $\boxed{3\sqrt {10} }{\text{ or }}\boxed{9.48}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Mensuration

Keywords: Cylinder, surface area of the cylinder, volume of the cylinder, right cylinder, height, radius depth.

Answer 2

3 k + 2 k = 5 k
5 k = 250
k  = 250 : 5 = 50
The length of longer piece is : 3 * 50 = 150 units