Find the missing side, the area and perimeter of a rectangle if one side is 9 inches and the diagonal is 15 inches

Question

Find the missing side, the area and perimeter of a rectangle if one side is 9 inches and the diagonal is 15 inches

Answer 1

We can see the right triangle with that diagonal. Then, we can use the Pythagorean Theorem.

a²+b²=c²

a=9

c=15

 

9²+b²=15²

81+b²=225

b²=144

b=12

 

So the sides are 9 inches and 12 inches. Now we can find the area and perimeter.

A=12*9

A=108 inches

 

P=9+9+12+12

P=42 inches

Answer 2

A rectangle has two pairs of parallel sides that are equal to each other.  If we draw a diagonal across the rectangle, we get two congruent right triangles.

 

Let x = the leg of a triangle

The hypotenuse is 15 inches

 

We can use Pythagorean theorem to find the missing side.  Let the missing side be y.

 

9² + y² = 15²

 

81 + y² = 225

        y² = 144

        y = √(144)

        y = 12

 

The missing side is 12 inches.

 

Perimeter = 2(length) + 2(width)

               = 2(9)  2(12)

               = 18 + 24

               = 42

 

The perimeter is 42 inches.

 

 

Area = length × width

        = 9 × 12

        = 108

 

The area is 108 square inches.