suppose you know the base of a rectangle has a length of 4 inches and a diagonal has a length of 5 inches. find the area of the rectangle.

Question

find the area of the recatangle

Answer 1

When a diagonal is drawn inside a rectangle, two congruent right triangles are formed.  The legs of the triangle are the sides of the rectangle.  We can use the Pythagorean theorem to find the missing side.

 

x² + 4² = 5²

 

If we know our Pythagorean triples, we can see that x is 3.  So the missing side is 3 inches.

 

To find the area of the rectangle, multiply the base side by the side we just found.

 

 

Area = 3 inches × 4 inches

 

Area = 12 square inches