Question

List the sides in order from shortest to longest in ∆PQR, with the measure of angle P=45, the measure of angle Q=10x+30, and the measure of angle R=5x

Answer 1

Answer:

PR > QR > PQ

Step-by-step explanation:

Given : angle P = 45°

angle Q = (10x+30)°

angle R = (5x)°

We know that the sum of all interior angles of a triangle is equal to 180°.

so, 45° + (10x+30)° + (5x)° = 180°

45+10x+30+5x = 180

75+15x = 180

15x = 180-75

15x = 105

x = 105/15 = 21/3

x = 7

Now, angle Q = (10x+30)°

= 10(7)+30

= 70+30

= 100°

angle R = 5x°

= 5(7)

= 35°

From above,

PR is the largest side because the side which is opposite to the largest angle is always large.

PQ is the smallest side because the side which is opposite to the smallest angle is always small.

So, the Order of sides from shortest to longest is : PR > QR > PQ