4 years ago

the length of a rectangle is 8 more than twice its width the perimeter is 96 ft find the dimensions of the rectangle

Mathematics

1 answer:

borishaifa [10]4 years ago

8 0

The width would equal 13 1/3. And the length would equal 34 2/3.

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The figure shows △XYZ. XW⎯⎯⎯⎯⎯⎯ is the angle bisector of ∠YXZ .<br><br> What is WZ ?

Mnenie [13.5K]

Use the law of cosines to find the measure of angle YXZ.

$8^2=6.5^2+6^2-2(6.5)(6)\cos(\angle YXZ)$
$\cos(\angle YXZ)\approx0.1827$
$\angle YXZ\approx 1.3871\text{ rad}\approx79.4734^\circ$

This means angles YXW and WXZ share the same measure of about $39.7367^\circ$ .

Use the law of cosines again to find the measure of angle XZW.

$6.5^2=8^2+6^2-2(8)(6)\cos(\angle XZW)$
$\cos(\angle XZW)\approx0.6016$
$\angle XZW\approx0.9253\text{ rad}\approx53.0181^\circ$

This means the measure of angle XWZ is

$180^\circ=\angle WXZ+\angle XWZ+\angle XZW\implies \angle XWZ\approx87.25^\circ$

Now using the law of sines, you have

$\dfrac{\sin(\angle WXZ)}{WZ}=\dfrac{\sin(\angle XWZ)}6\implies WZ\approx3.84$