Question

Please help. I’ll mark you as brainliest if correct!

One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is ___ m.

Answer 1

Answer:

The other leg is 4 m long, and the hypotenuse is 5 m long

Step-by-step explanation:

Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:

$hyp^2=leg_1^2+leg_2^2$

so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"

So we can assume that the largest of this is the hypotenuse: "x+1"

Not, they must verify the Pythagorean identity:

$hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4$

then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m