The length of a rectangle is (x + 5) inches long, and the width is 3 2/5 inches. If the area is 51 square inches. Write and solve and equation to find the length of the rectangle

Length = 15 inches

Step-by-step explanation:

Let L represent the Length, W, the width and A, the area of the rectangle

from the question;

L = x + 5 ... eq 1

W = 3 2/5

Changing the value of W into an improper fraction; W = 17/5

A = 51 inches

Area of a rectangle, A = Lenght x Width

A = L X W ... eq 2

slotting the values of A, L and W in eq 2

51 = (x + 5) X 17/5

51 = (17/5x) + (17/5 X 5)

51 = 17/5x + 17

51 = 17x + 85

5

Cross multiply

5 X 51 = (17x + 85) X 1

255 = 17x + 85

Subtracting 85 from both sides

255 - 85 = 17x + 85 - 85

170 = 17x

Dividing both sides by the coefficient of x which is 17

10 = x

Therefore, x = 10

Slotting in the value of x in eq 2

L = 10 + 5

L = 15 inches

Let's check our answer by slotting in the values of A, W and L in eq 1

51 = 15 X 17/5

51 = 3 X 17

51 = 51

Since both sides of the equation are equal, the value of L is correct