i need to figure out the equatin for this .

Question

A rectangle is drawn so the width is 1 inches longer than the height. If the rectangle's diagonal measurement is 5 inches, find the height.

Give your answer rounded to 1 decimal place,

 

Answer 1

You can use the Pythagorean equation (a² + b²= c²) because the triangle the diagonal and the 2 sides make is a right triangle.

h = height of rectangle
h+1 = width of rectangle

h²+(h+1)²=5²

2h²+2h+1=25

h=-4 or h=3 since the height can't be negative, the only answer is that the height is 3in.

Hope this helps.

Answer 2

Right away, I thought of the 3-4-5 right triangle.  Hypotenuse 5 is the diagonal; the legs are 3 & 4 and these satisfy the "width is 1 inch longer than height" criterion.

 

OK, if you did not have that insight, here's an algebra approach:  The diagonal forms a right triangle; label its sides x & x+1, and hypotenuse 5.  Use Pythagorean Theorem to get x² + (x+1)² = 5² which leads to 25 = 2x² +2x + 1, and so forth.  The only positive solution is x = 3.