The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

1 Answer
Oct 14, 2015

Answer:

The height (length) is #"24 cm"#.

Explanation:

http://gifsgallery.com/right+triangle+gif?image=212188146

The diagonal of a right triangle is the hypotenuse and is designated as side #c#. The width of a right triangle is side #b#, and the height is side #a#. You are looking for side #a#.

The Pythagorean equation is #c^2=a^2+b^2#.
#c="25 cm"#
#b="7 cm"#
#a=?#

Rearrange the equation to solve for side #a#.

#a^2=c^2-b^2#

Substitute the known values into the equation.

#a^2=(25"cm")^2-(7"cm")^2=#

#a^2=625"cm"^2"-"49"cm"^2=#

#a^2=576"cm"^2#

Take the square root of both sides.

#sqrt(a^2)=sqrt(576"cm"^2")#

#a="24 cm"#