31.Two ships leave port at the same time,
one heading due south and the other
heading due east. Several hours later,
they are 170 mi apart. If the ship travel-
ing south traveled 70 mi farther than the
other ship, how many miles did they
each travel?
32.Deborah Israel is flying a kite that is 30 ft
farther above her hand than its horizon-
tal distance from her. The string from
her hand to the kite is 150 ft long. How
high is the kite?
528 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
Port
Ship
x + 70
x
E
S
Ship
x
30 + x
33.A game board is in the shape of a right triangle. The hypotenuse is 2 inches longer than
the longer leg, and the longer leg is 1 inch less than twice as long as the shorter leg. How
long is each side of the game board?
34.Manuel Bovi is planting a vegetable garden in the shape of a right triangle. The longer leg
is 3 ft longer than the shorter leg, and the hypotenuse is 3 ft longer than the longer leg.
Find the lengths of the three sides of the garden.
35.The diagonal of a rectangular rug measures 26 ft, and the length is 4 ft more than twice
the width. Find the length and width of the rug.
36.A 13-ft ladder is leaning against a house. The distance from the
bottom of the ladder to the house is 7 ft less than the distance
from the top of the ladder to the ground. How far is the bottom of
the ladder from the house?
Solve each problem. See Example 4.
x
x – 7
13
37.A club swimming pool is 30 ft wide and
40 ft long. The club members want an
exposed aggregate border in a strip of
uniform width around the pool. They
have enough material for How
wide can the strip be?
38.Lyudmila Slavina wants to buy a rug for
a room that is 20 ft long and 15 ft wide.
She wants to leave an even strip of floor-
ing uncovered around the edges of the
room. How wide a strip will she have if
she buys a rug with an area of 234 ft^2?
296 ft^2.
39.A rectangle has a length 2 m less than twice its width. When 5 m are added to the width,
the resulting figure is a square with an area of 144. Find the dimensions of the original
rectangle.
40.Mariana Coanda’s backyard measures 20 m by 30 m. She wants to put a flower garden in
the middle of the yard, leaving a strip of grass of uniform width around the flower garden.
Mariana must have 184 of grass. Under these conditions, what will the length and
width of the garden be?
m^2
m^2
40 ft
30 ft Pool
15 ft
20 ft
15 ft Rug
