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# Part A: What is the length of diagonal AM?

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Part A: What is the length of diagonal AM?

Part B: What is the length of diagonal FR?

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Mar 5, 2019

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Don't think we can solve this one without some other info, Josey......   Mar 5, 2019
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This is rhombus FARM with a side length of 7 yards. The measure of ∠AFM is 60°

JoseyP  Mar 5, 2019
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OK...we got something we can work with...

If AFM is 60°.....then angle RFM =  30°

And the top left triangle is a 30-60-90 right triangle

And the side opposite the 90°  angle is the side of 7

And the side opposite the 30° angle is 1/2 the side length = 1/2*7 =  3.5

So... 1/2 of diagonal MA =  1/2(7) = 3.5

So....the whole length of AM is twice this = 7 units

And angle FMR is supplemental to angle AM =  120°

Then angle AMR is 1/2 of this = 60°

And the bottom left triangle is also 30-60-90

The side opposite  the 60° angle  = 3.5sqrt(3) units

And this is 1/2 the length  of diagonal  FR

So..its length = 2 *3.5sqrt(3)  =  7sqrt (3) units   Mar 5, 2019