Download Systems of Equations

Honors Geometry
Unit 5 – PS
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Systems of Equations
Solve each problem
USING TWO EQUATIONS IN TWO VARIABLES.
Show all work!
Problem 1:
The length of a rectangular garden is three times the width. If
the perimeter is 32 m, what are the dimensions of the garden?
Problem 2:
Two sides of a triangle have the same length. The remaining
side is one-third as long as each of the other sides. If the
perimeter of the triangle is 315 cm, what is the length of each
side?
Systems PS.doc
Fricker, Evans, Cendrowski
Lower Moreland HS
Honors Geometry
Unit 5 – PS
Page 2
Problem 3:
Two angles are supplementary. The measure of one of these
angles is 12˚ less than one third the measure of the other.
What is the measure of each angle?
Problem 4:
Two angles are supplementary. The sum of the measures of
the larger angle and twice the smaller angle is 265˚. Find the
measure of the larger angle.
Systems PS.doc
Fricker, Evans, Cendrowski
Lower Moreland HS
Honors Geometry
Unit 5 – PS
Page 3
Problem 5:
Sarah purchased two picture frames. The perimeter of the
larger frame is 240 cm, and the perimeter of the smaller frame
is 140 cm. The height of the smaller frame is the same as the
width of the larger frame, and the width of the smaller frame is
10 cm less than the height of the smaller frame. Find the
dimensions of the larger frame.
Solve each of the following problems by
FACTORING A QUADRATIC EQUATION.
Show all work!
Problem 6:
A picture frame of uniform width surrounds a 30 cm by 20 cm
picture. The combined area of the picture and frame is 2000
square centimeters. What is the width of the frame?
Systems PS.doc
Fricker, Evans, Cendrowski
Lower Moreland HS
Honors Geometry
Unit 5 – PS
Page 4
Problem 7:
The width of a rectangle is 7 m less than twice the length. The
area of the rectangle is 30 square meters. Find the length of
the rectangle.
Problem 8:
A rectangular picture is 4 cm longer than it is wide. It is
surrounded by a mat that is 2 cm wide. The combined area of
the picture and the mat is 140 cm2. Find the dimensions of
the picture.
Systems PS.doc
Fricker, Evans, Cendrowski
Lower Moreland HS
Honors Geometry
Unit 5 – PS
Page 5
Problem 9:
A side of a house is in the shape of a triangle on top of a
rectangle. The rectangle is four times as long as it is high, and
the altitude of the triangular part is 1 m greater than the
height of the rectangle. The total area of the side of the house
is 60 square meters. Find the height of this side of the house.
Problem 10:
Dan owns a vacant lot that is 32 m wide and 40 m long. He
makes a rectangular basketball court in the middle by
subtracting equal amounts from the length and width. The
area of the court is 560 square meters. How far from the edge
of the lot is an edge of the court?
Systems PS.doc
Fricker, Evans, Cendrowski
Lower Moreland HS