+0

# geometry

0
34
3

The perimeter of an isosceles triangle is 36 centimeters and two sides of the triangle are in the ratio 2:7. What is the number of centimeters in the length of the longest side?

Oct 14, 2020

#1
+1

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

Possible combos:

2x + 7x    < 36-9x

18x < 36

x < 2

x =1      2   7  27

x=2      4 14  18                   These do not meet the triangle inequality theorem above

x = 1.5         5   17.5   13.5  <====  possible          5:17.5   =  2:7             longest = 17.5 cm

Oct 15, 2020
#2
+2

The perimeter of an isosceles triangle is 36 centimeters and two sides of the triangle are in the ratio 2:7. What is the number of centimeters in the length of the longest side?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An isosceles triangle is a triangle with two equal sides.

If the ratio of the two sides is 2:7 then the ratio of all 3 sides is 2:7:7

The length of the longest side is:>         7(36 / 16) = 15.75 cm

Oct 15, 2020
edited by Dragan  Oct 15, 2020
#3
+1

Agree!   Sorry....didn't see 'isosceles' in the Q !     ~ EP

ElectricPavlov  Oct 15, 2020