Homework 1.5

1.  A rectangular piece of metal is 9 in. longer than it is wide. Squares with sides 3 in. long are cut from the four​ corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 76 in.3​?

Choose the correct answer below.

1. (x+3)(x−6)=76
2. x(x+9)=76
3. (x+3)(x−6)(3)=76
4. $x\left(x+9\right)\left(3\right)=76$

2.  Find two consecutive integers whose product is 30.

1. −7, −6
2. 5​, 6 and −6, −5
3. 5​, 6
4. 6​, 7 and -7, -6

3 .  The product of two consecutive even integers is 168.

Find the integers.

The positive integers are _____  (Use a comma to separate answers as​ needed.)

The negative integers are ____

4.   One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is ______m.

The length of the hypotenuse is ____ m.

5.  The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 269 in2.

Find the lengths of the sides of the two squares.

A side of the small square is ____ ​in.; a side of the big square is _____ in.

6.  The area of a rectangular wall of a barn is 100 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

width = ____ft

length = ____ft

7.   Solve.  The area of a square is 32 more than its perimeter. Find the length of a side.

The length of a side of the square is ____ units.

8.   A building is 1 ft from a 12​-ft fence that surrounds the property. A worker wants to wash a window in the building 15 ft from the ground. He plans to place a ladder over the fence so it rests against the building.​ (See the​ figure.) He decides he should place the ladder 12 ft from the fence for stability. To the nearest tenth of a​ foot, how long a ladder will he​ need?

He will need a _____ ft ladder.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)