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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q35. (page 433)

The area of a rhombus is 100. Find the length of the two diagonals if one is twice as long as the other.

Short Answer

Expert verified

The length of two diagonals of the rhombus are 10 and 20.

Step by step solution

01

Step 1. Analyze the given information.

Given area of rhombus $A = 100$

Let the diagonals be $d_{1}$ and $d_{2}$

According to the question the length of two diagonals if one is twice as long as others, which means

$d_{1} = 2 d_{2}$

02

Step 2. Concept Used.

Area of rhombus can be found using the formula

$A = \frac{1}{2} d_{1} d_{2}$

Where $d_{1}$ and $d_{2}$ are the diagonals of the rhombus.

03

Step 3. Use formula of the area of rhombus.

$\begin{array}{l} A = \frac{1}{2} d_{1} d_{2} \\ A = \frac{1}{2} (2 d_{2}) (d_{2}) \\ 100 Invalid <m:msup> element = \\ d_{2} = 10 \end{array}$

So, the another diagonal will be

$\begin{array}{l} d_{1} = 2 d_{2} \\ d_{1} = 2 (10) \\ d_{1} = 20 \end{array}$

Therefore, the length of the diagonals are10 and 20.

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