4. The interior angles of a triangle are 60°, 45° and 75°. The shortest side is 10 cm less than the longest side. Determine the perimeter of the triangle to the nearest cm.

Step-by-step explanation:

The length of each side corresponds to the sizes of each angle respectively.

To determine the length of each side, we would apply sine rule which is expressed as

a/sinA = b/SinB = c/SinC

The diagram of the triangle is shown in the attached photo. The longest side is c. If the shortest side is 10 cm less than the longest side, it means that the length of the shortest side is c - 10

Therefore,

c/Sin75 = (c - 10)/Sin45

c/0.966 = (c - 10)/0.707

Cross multiplying, it becomes

c × 0.707 = 0.966(c - 10)

0.707c = 0.966c - 9.66

0.966c - 0.707c = 9.66

0.259c = 9.66

c = 9.66/0.259

c = 37.3 cm

The shortest side is

37.3 - 10 = 27.3 cm

Applying the sine rule again,

b/Sin60 = 37.3/Sin75

b/0.866 = 37.3/0.966

Cross multiplying, it becomes

0.966b = 0.866 × 37.3

b = 32.3018/0.966

b = 33.4 cm

The perimeter is

27.3 + 33.4 + 37.3 = 98 cm

i would say the third one.

step-by-step explanation: liner would mean in a line and the only one that doesn't look like it's even thinking about forming a line would be the third one