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