Question

Please help me with this geometry question

Answer 1

$\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star$

• HJ = 23.5 in

$\textsf{ \underline{\underline{Steps to solve the problem} }:}$

Take HJ = x, GH = y and GJ = z

• x = y + 2

• z = x + y - 17

• x + y + z = 73

put the value of x from equation 1 in equation 2

${ \qquad❖ \: \sf \:z = (y + 2) + y - 17}$

${ \qquad❖ \: \sf \:z = 2y - 15}$

now, put the value of x and z in equation 3

${ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73}$

${ \qquad❖ \: \sf \:4y - 13 = 73}$

${ \qquad❖ \: \sf \:4y = 86}$

${ \qquad❖ \: \sf \:y = 21.5 \: \: in}$

Now, we need to find HJ (x)

${ \qquad❖ \: \sf \:x = y + 2}$

${ \qquad❖ \: \sf \:x = 21.5 + 2}$

${ \qquad❖ \: \sf \:x = 23.5 \: \: in}$

${ \qquad \large \sf {Conclusion} :}$

• HJ = 23.5 in