Question 1177732
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(1) Use Heron's formula to find the area of triangle ABC.<br>
The semiperimeter is<br>
{{{(32+26+10)/2 = 34}}}<br>
The area is<br>
{{{sqrt((34)(34-32)(34-26)(34-10)) = sqrt((34)(2)(8)(24)) = 16*sqrt(51)}}}<br>
(2) Use the area and the base AB to find the height CH.<br>
{{{16*sqrt(51) = 32(CH)/2}}}
{{{CH = sqrt(51)}}}<br>
(3) Use the height CX and the length of BC to find the length of BH.<br>
{{{(BH)^2 = 10^2-(sqrt(51))^2 = 100-51 = 49}}}
{{{BH = 7}}}<br>
(4) Use BH and BM to find HM.<br>
{{{HM = 16-7 = 9}}}<br>
ANSWER: HM = 9<br>