The perimeter of a triangle with two equal sides is 71 cm. if its base were lengthened by 6 cm and each leg were shortened by 4 cm, all three sides would be equal. find the length of the base of the original triangle.

Your answer would be 17cm.

Because two sides are equal, we can label these two sides x, and the base y, and since the perimeter is 71cm, we can then write the equation 2x + y = 71.

Then we apply the changes made to our sides, so the two equal sides would become x - 4, and the base would become y + 6. We can now set these equal to each other as it states that all sides are equal when this change occurs.

Now we have a pair of simultaneous equations that we can solve with substitution firstly by rearranging the equation x - 4 = y + 6 to get x:

x - 4 = y + 6

+ 4

x = y + 10

Now we can substitute (y + 10) as x into the equation 2x + y = 71 :

2(y + 10) + y = 71

2y + 20 + y = 71

3y + 20 = 71

- 20

3y = 51

÷ 3

y = 17

I hope this helps!

cant open file sorry!

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: