Chapter 7.2, Problem 16PSB

Solution

a.

The perimeter of $\Delta GHJ$

The perimeter of $\Delta GHJ$ is $72.5$

Given: Perimeter of $\Delta DEF$ is $145$

Concept used: Here, we are using the mid-point theorem.

Calculation: Since, G, H and J are the mid-points of DF, FE and DE respectively.

GH = $\frac{DE}{2}$

HJ = $\frac{DF}{2}$

GJ = $\frac{EF}{2}$

So, the perimeter of $\Delta GHJ$ is half the perimeter of $\Delta DEF$

Hence, perimeter of $\Delta GHJ$ = $\frac{145}{2}$

➔ $72.5$

Conclusion: Hence, the perimeter of $\Delta GHJ$ is $72.5$

b.

Generalization based on the solution of part (a)

  $\Delta GHJ$ will have half of the perimeter of $\Delta DEF$

Given: Perimeter of $\Delta DEF$ is $145$

Explanation: Generalization is that a triangle is formed by connecting the mid-points of the sides of a larger triangle will have half its perimeter.