One leg of a right triangle has a length of 55 m. the other sides have lengths that are consecutive integers. find these lengths.

First let us assign the variables for the two lengths:

x = 1st integer

x + 1 = 2nd consecutive integer = the hypotenuse of the right triangle

The 2nd consecutive integer should be the hypotenuse since its value should be highest among the three sides.

Now using the hypotenuse formula we calculate for x:

(x + 1)^2 = 5^2 + x^2

x^2 + 2x + 1 = 25 + x^2

2x + 1 = 25

2x = 24

x = 12 m

So other integer is

 x + 1 = 13 m

Therefore the other sides are 12 m and 13 m.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!