Studdy AI Logo
Math

QuestionFind FHF H given FG=6xF G=6 x, GH=x+16G H=x+16, and FH=8x+11F H=8 x+11. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The length of line segment FG is6x. The length of line segment GH is x+163. The length of line segment FH is8x+114. The line segments FG, GH, and FH are all part of the same straight line.

STEP 2

According to the properties of a straight line, the sum of the lengths of two smaller line segments (FG and GH) should be equal to the length of the larger line segment (FH). We can write this as an equationFG+GH=FHFG + GH = FH

STEP 3

Now, plug in the given values for FG, GH, and FH into the equation.
6x+(x+16)=8x+116x + (x+16) =8x +11

STEP 4

implify the left side of the equation by combining like terms.
7x+16=8x+117x +16 =8x +11

STEP 5

Rearrange the equation to isolate the variable x on one side. Subtract7x from both sides of the equation.
16=x+1116 = x +11

STEP 6

Subtract11 from both sides of the equation to solve for x.
x=16−11x =16 -11

STEP 7

Calculate the value of x.
x=16−11=5x =16 -11 =5

STEP 8

Now that we have the value of x, we can substitute it back into the equation for FH to find the length of FH.
FH=8x+11FH =8x +11

STEP 9

Substitute x =5 into the equation for FH.
FH=8(5)+11FH =8(5) +11

STEP 10

Calculate the value of FH.
FH=8(5)+=40+=51FH =8(5) + =40 + =51So, the length of line segment FH is51.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord