Question

A ladder $25$ feet long is leaning against a wall so that the foot of the ladder is $7$ feet from the base of the wall. If the bottom of the ladder is moved out another $8$ feet from the base of the wall, how many feet will the top of the ladder move down the wall?[asy]

size(150);

draw((0,0)--(0,27));
draw((0,24)--(7,0));
draw(rightanglemark((-1,0),(0,0),(0,1),40));
label("$7$ ft",(3.5,0),S);
label("$8$ ft",(11,0),S);
draw((8,1)--(14,1),EndArrow(4));
label("$x$ ft",(-1,22),W);
draw((-1,25)--(-1,19),EndArrow(4));
label("wall",(0,10),W);
label("$25$-ft ladder",(3.5,12),NE);

drawline((0,0),(1,0));
[/asy]

Answer 1

Answer: 4 ft

Explanation:

It went from 7 to 15 for the bottom of a right triangle.

your hypotenuse is 25 (length of ladder)

use Pythagorean theorem

25² = 7² + y²

y =24

25²=15² + y²

y=20

so it went from 24 to 20 the difference is 4 ft