Prove that 3:8 is equivalent to 12:32:
I'd suggest that you write the ratio 12:32 as<span /><span><span><span><span><span><span><span><span><span>12</span><span /></span><span><span>32</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span></span>
and then factor both the 12 and the 32. Write out the factors:<span /><span><span><span><span><span><span><span><span><span>12</span><span /></span><span><span>32</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span><span>(</span><span>?</span><span>)</span><span>(</span><span>?</span><span>)</span></span><span /></span><span><span><span>(</span><span>?</span><span>)</span><span>(</span><span>?</span><span>)</span></span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span></span> and then reduce this last result by cancelling out the common factor.3 x 4 = 12
8 x 4 = 32
It is equivalent. They both multiplied by four the get that ratio.
Since angles that add up to make a line add up to 180 degrees, you know
Angle ACD + angle ACB=180
Since it tells you ACD is 100, substitute that in.
100+ACB=180
ACB=80
Next, the sum of all the interior angles in a triangle is 180.
ACB+A+B=180.
Substitute in the values you know.
80+A+60=180
A=40
Angle a is 40 degrees.
Hope this helps!
Hi there!
Let the width of the rectangle be called x. Then the length of the rectangle is 2x. We get the following perimeter:
Collect the terms
Divide by 6
Therefore, the width of the rectangle is 21 feet and the length is 2 × 21 = 42 feet.
The answer is -4x+64+2x^2