Question

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15. 7 inches, so the equation to solve is 2a b = 15. 7. If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b?

a. –2 in.
b. 0 in.
c. 0. 5 in.
d. 2 in.
e. 7. 9 in.

Answer 1

C and D

Explanation:

The perimeter would be equal to 2a + b = 15.7 inches

You can automatically get rid of the first two answers (a) and (b).

You cannot have a side of a triangle being a negative value or 0.

So that leaves you with (c), (d) or (e) as answers for side b.

Subtract each of these answers from the perimeter value.

(c) 15.7 - 0.5 = 15.2

(d) 15.7 - 2 = 13.7

(e) 15.7 - 7.9 = 7.8

Since you know the length of the two remaining side have to be equal, you can divide the above numbers by two and that will give you the values for side a.

(c) 15.2 / 2 = 7.6

(d) 13.7 / 2 = 6.85

(e) 7.8 / 2 = 3.9

Check whether these these values now fit the rule that says the sum of any two sides must be greater than the third side. So:

Side a(1) + Side a(2) must be greater than Side b

Side a(1) + Side b must be greater than Side a(2)

(c) 7.6 + 7.6 > 0.5? yes, 7.6 + 0.5 > 7.6? yes - So this answer is correct

(d) 6.85 + 6.85 > 2? yes, 6.85 + 2 > 6.85? yes - So this answer also works

(e) 3.9 + 3.9 > 7.9? NO, 3.9 + 7.9 > 3.9? yes - This answer does not work