Question 615015
Try this!
{{{A[1] = (1/2)bh}}} The original area.
{{{A[2] = (1/2)(2b)*(1/2)h}}} The new area when the base is doubled and the height is halved.
{{{A[2] = (1/2)bh}}} = {{{A[1]}}} The area remains the same!
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{{{A[1] = (1/2)bh}}} The original area.
{{{A[2] = (1/2)(2b)h}}}
{{{A[2] = bh}}} = {{{2A[1]}}} The area is doubled when the base is doubled but the height remains the same!
Using 10 for the base, ie, b = 10, we have:
{{{A[1] = (1/2)bh}}} Substitute b = 10.
{{{A[1] = (1/2)10*h}}}
{{{A[1] = 5h}}} Now double the base (2*10 = 20) and halve the height (h/2), we get:
{{{A[2] = (1/2)(20)(1/2)h}}} Simplify.
{{{A[2] = 5h}}} The area remains the same!
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{{{A[1] = (1/2)bh}}} Double the base (2*10 = 20) but leave the height alone.
{{{A[2] = (1/2)(20)*h}}} Simplify.
{{{A[2] = 10h}}} The area is doubled!
If you want, you can use any number for the height but the results will be the same.