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3 years ago

Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form.

Mathematics

2 answers:

ololo11 [35]3 years ago

7 0

Answer: Perimeter = 22*sqrt(2)

Area = 60.5 inches

Step-by-step explanation:

Simple a square has 4 equal sides.

It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

Serjik [45]3 years ago

4 0

Answer:

4* $\sqrt{60.5}$ is peremiter and 60.5 is area

Step-by-step explanation:

11x11=121/2=60.5

$\sqrt{60.5}$ =one side of square

4* $\sqrt{60.5}$ =peremiter

60.5=area

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$v(x,y)=\dfrac xy$

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

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Note that we need to use the Jacobian in the other direction; that is, we've computed

$\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}$

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we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
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