Question

Someone please help me with this question asap!

Answer 1

Answer:

23.5 in

Step-by-step explanation:

To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.

Equation 1

HJ is two inches longer than GH:

⇒ HJ = GH + 2

Equation 2

GJ is 17 inches shorter than the sum of HJ and GH:

⇒ GJ + 17 = HJ + GH

Equation 3

The perimeter of ΔGHJ is 73 inches:

⇒ HJ + GH + GJ = 73

Substitute Equation 1 into Equation 2 and isolate GJ:

⇒ GJ + 17 = GH + 2 + GH

⇒ GJ + 17 = 2GH + 2

⇒ GJ = 2GH - 15

Substitute Equation 1 into Equation 3 and isolate GJ:

⇒ GH + 2 + GH + GJ = 73

⇒ 2GH + GJ = 71

⇒ GJ = 71 - 2GH

Equate the two equations where GJ is the subject and solve for GH:

⇒ 2GH - 15 = 71 - 2GH

⇒ 4GH = 86

⇒ GH = 21.5

Substitute the found value of GH into Equation 1 and solve for HJ:

⇒ HJ = 21.5 + 2

⇒ HJ = 23.5

Answer 2

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

• Correct choice = B

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

Take HJ = a, GH = b and GJ = c

• a = b + 2

• c = a + b - 17

• a + b + c = 73

put the value of a from equation 1 in equation 2

$\qquad❖ \: \sf \:c = (b + 2) + b - 17$

$\qquad❖ \: \sf \:c = 2b - 15$

now, put the value of a and c in equation 3

$\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73$

$\qquad❖ \: \sf \:4b - 13 = 73$

$\qquad❖ \: \sf \:4b = 86$

$\qquad❖ \: \sf \:b = 21.5 \: \: in$

Now, we need to find HJ (a)

$\qquad❖ \: \sf \:a = b + 2$

$\qquad❖ \: \sf \:a = 21.5 + 2$

$\qquad❖ \: \sf \:23.5 \: \: in$

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

• Option B is correct