Chapter 3, Problem 17RP

To determine

To calculate: The perimeter of $\Delta FHJ$

Answer to Problem 17RP

The perimeter of $\Delta FHJ$ is $60$

Explanation of Solution

Given information: $\Delta FJH$ is isosceles with base $\overline{JH}$ , K and G are mid-points, $FK=2x+3$ , $GH=5x-9$ and $JH=4x$ are provided in the question which will help to find the solution.

Calculation: Here, FJ = FH ( $\because$

  $\Delta FJH$ is isosceles)

And, $\angle FHJ=\angle FJH$ (angle opposite to equal sides are equal)

And, FK = KJ ( $\because$ K is mid-point of FJ)

Similarly, FG = GH ( $\because$ G is mid-point of FH)

Hence, FJ = FH

  $FK+KJ=FG+GH$

  →$2(2x+3)=2(5x-9)$

  →$12=3x$

  →$x=4$

So that, perimeter is $FJ+JH+HF$ of $\Delta FHJ$

  $2(5\times 4-9)+2(2\times 4+3)+4\times 4$

  →$2(20-9)+2(8+3)+16$

  →$22+22+16$

  →$60$

Conclusion: Hence, the perimeter of $\Delta FHJ$ is $60$