A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

Answer 1

Length of longer diagonal is #22.89 unit #

We know the area of the parallelogram as #A_p=s_1*s_2*sin theta or sin theta=24/(15*8)=0.2 :. theta=sin^-1(0.2)=11.54^0:.#consecutive angles are supplementary #:.theta_2=180-11.54=168.46^0#.

Longer diagonal can be found by applying cosine law:#d_l= sqrt(s_1^2+s_2^2-2*s_1*s_2*costheta_2)=sqrt(15^2+8^2-2*15*8*cos168.46) =22.89 unit #[Ans]

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Answer 2

Claire Akin

The length of the longest diagonal of the parallelogram can be found using the formula ( \text{Diagonal} = \sqrt{(a^2 + b^2)} ), where ( a ) and ( b ) are the lengths of the sides of the parallelogram. In this case, ( a = 15 ) and ( b = 8 ). Plugging these values into the formula gives:

( \text{Diagonal} = \sqrt{(15^2 + 8^2)} ) ( \text{Diagonal} = \sqrt{(225 + 64)} ) ( \text{Diagonal} = \sqrt{289} ) ( \text{Diagonal} = 17 )

Therefore, the length of the longest diagonal of the parallelogram is 17 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.