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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 rhombusA=100

Let the diagonals bed1andd2

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

d1=2d2

02

Step 2. Concept Used.

Area of rhombus can be found using the formula

A=12d1d2

Whered1 and d2are the diagonals of the rhombus.

03

Step 3. Use formula of the area of rhombus.

A=12d1d2A=12(2d2)(d2)100Invalid <m:msup> element=d2=10

So, the another diagonal will be

d1=2d2d1=2(10)d1=20

Therefore, the length of the diagonals are10 and 20.

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