Exercise 43 Page 388

Let's analyze the given figure.

We are given that the adjacents sides with lengths n and 3m are congruent. Therefore, by the definition of congruence, we know that their lengths are equal. n = 3mWe also know that sides whose lengths are n + 6 and 7m - 14 are congruent, so their lengths are equal. n + 6 = 7m - 14 Let's substitute 3m for n in the above equation, and solve it for m.

n + 6 = 7m - 14

Substitute

n= 3m

3m + 6 = 7m - 14

▼

Solve for m

SubEqn

LHS-6=RHS-6

3m = 7m - 20

SubEqn

LHS-7m=RHS-7m

- 4m = - 20

DivEqn

.LHS /(- 4).=.RHS /(- 4).

m = - 20/- 4

DivNegNeg

- a/- b=a/b

m = 5

Now, let's find the value of n. To do so, we will substitute m=5 in the equation n=3m.

n = 3m

Substitute

m= 5

n = 3( 5)

Multiply

Multiply

n = 15

Now that we found the values of n and m, we can find the lengths of the sides. To do so, we will substitute m= 5 and n= 15 in the expressions for the side lengths.

Side length	Substitute	Simplify
3m	3( 5)	15
n	15	15
n + 6	15 + 6	21
7m - 14	7( 5) - 14	21

The lengths of the sides are 15, 15, 21, and 21.