The length of a standard jewel case is 3 cm more than its width. The area of the rectangular top of the case is 304 cm squared. Find the length and width of the jewel case.

width = 16 cm

length = 19 cm

Step-by-step explanation:

Let the width be x cm.

Given that length is 3 cm more than width then

length =  x+3 cm

area of rectangle = 304 square cm. -----1

area of rectangle is given by

area =length * width

substituting from equation 1 and length and width in terms of x we have

304 = x(x+3)

As length cannot be negative hence x = 16

Thus width = x = 16 cm

length = x+3 = 16+3 = 19 cm

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

ddd

step-by-step explanation: