math

Problem of the Week

Alternate Dimensions

The four shapes to the right are each drawn
with a horizontal base and a vertical height.
Figure A is a right-angled triangle, Figure B
is an isosceles triangle, Figure C is a square,
and Figure D is a rectangle. The figures are
not drawn to scale.

Using the following clues, determine the measure of the (horizontal) base and the
measure of the (vertical) height of each figure.
1. The measure of the base of Figure A is the same as the measure of the base
of Figure D.
2. The measure of the base of Figure A is one unit less than the measure of the
base of Figure B.
3. The side length of Figure C is the same as the measure of the base of
Figure A.
4. The measure of the height of Figure B is the same as the measure of the
height of Figure A and also the same as the measure of the base of Figure B.
5. The area of Figure C is 9 square units.
6. The total area of all four figures is 38 square units.

  1. 👍 0
  2. 👎 0
  3. 👁 89
  1. A = the total area of all four figures

    AA = the area of a right-angled triangle

    AB = the area of a an isosceles triangle

    AC = the area of a an square

    AD = the area of a rectangle

    LA = the measure of the base of Figure A

    LB = the measure of the base of Figure B

    LC = the measure of the base of Figure C

    LD = the measure of the base of Figure D

    LC = the side length of Figure C

    hA = measure of the height of Figure A

    hB =measure of the height of Figure B

    hD = measure of the height of Figure D

    Clues:

    1.

    The measure of the base of Figure A is the same as the measure of the base of Figure D mean:

    LA = LD

    2.

    The measure of the base of Figure A is one unit less than the measure of the base of Figure B mean:

    LA = LB - 1

    3.

    The side length of Figure C is the same as the measure of the base of Figure A mean:

    LC = LA

    4.

    The measure of the height of Figure B is the same as the measure of the height of Figure A and also the same as the measure of the base of Figure B mean:

    hB = hA = LB

    5.

    5. The area of Figure C is 9 square units mean:

    LC² = 9

    So:

    LC² = √9

    LC = 3

    LC = LA

    LA = LC

    LA = 3

    LA = LB - 1

    3 = LB - 1

    Add 1 to both sides

    4 = LB

    LB = 4

    LA = LD

    LD = LA

    LD = 3

    hB = hA = LB

    hA= LB

    hA = 4

    hB = LB

    hB = 4

    6.

    AA = area of a right-angled triangle

    AB = area of a an isosceles triangle

    AC = area of a an square

    AD = area of a rectangle

    A = AA + AB + AC + AD = 38

    AA = LA ∙ hA / 2

    AA = 3 ∙ 4 / 2 = 12 / 2

    AA = 6

    AB = LB ∙ hB / 2

    AB = 4 ∙ 4 / 2 = 16 / 2

    AB = 8

    AC = 9

    AD = LD ∙ hD

    AD = 3 ∙ hD

    The total area of all four figures:

    A = area of a right-angled triangle + area of a an isosceles triangle + area of a an square + area of a rectangle = 38

    A = AA + AB + AC + AD = 38

    6 + 8 + 9 + 3 hD = 38

    23 + 3 hD = 38

    Subtract 23 to both sides

    3 hD = 15

    Divide both sides by 3

    hD = 5

    AD = LD ∙ hD

    AD = 3 ∙ 5

    AD = 15

    Results:

    AA = the area of a right-angled triangle = 6

    AB = the area of a an isosceles triangle = 8

    AC = the area of a an square = 9

    AD = the area of a rectangle = 15

    LA = the measure of the base of Figure A = 3

    LB = the measure of the base of Figure B = 4

    LC = the side length of Figure C = 3

    LD = the measure of the base of Figure D = 3

    hA = measure of the height of Figure A = 4

    hB =measure of the height of Figure B = 4

    hD = measure of the height of Figure D = 5

    1. 👍 0
    2. 👎 0
  2. One my typo:

    It should not be written like this:

    So:

    LC² = √9

    It should be written like this:

    So:

    LC = √9

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    1. Which angles are adjacent angles? (1 point) ∠GBM and ∠FBC ∠CBX and ∠FBC ∠XBG and ∠FBC ∠MBY and ∠FBC 2. The measure of ∠3 is 101°. Find the measure of ∠1. (1 point) 101° 106° 74° 79° 3. Is line l

    asked by christian on February 3, 2014
  2. Art

    Artists make shapes in the background smaller than shapes in the foreground to communicate their distance from the viewer.How else might a landscape artist show shapes in the background to depict their distance from the viewer?

    asked by CookieMonster on March 27, 2015
  3. Math (Basic)

    "A woman earns 10.00 per hour at her job, but if she works more than 20 hours in a week she is paid 1.5 times her regular salary for the overtime hours worked. One week her gross pay was 275. How many overtime hours did she work

    asked by Kai on June 24, 2011
  4. math

    Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of greater length than the speech she gave the week before. The table below show the length of several of her speeches: WK #/Length of

    asked by Jane on April 29, 2013
  5. Math

    How many rectangles can be drawn with 38 cm as perimeter? Also, find the dimensions of the rectangle whose area will be maximum.

    asked by Tanay on March 5, 2017
  1. Math

    Mrs. Jones recorded the time, in minutes, she spends reading each day for two weeks. The results are shown. What is the IQR for each week? Week 1 81 50 63 58 39 72 104 Week 2 62 54 110 72 68 34 79 A. The IQR for Week 1 is 65, and

    asked by Matt on March 18, 2020
  2. Reading

    Establish a Running Plan A 5-kilometer race is a little over 3 miles long. It is best to start by running a shorter distance and then gradually increase your running distance. This chart will help you to establish a running plan

    asked by Lili on May 10, 2019
  3. ART please help!!

    Go to internet explorer and type "lighthouse by by george seurat" (just like that) go to images it is the first one there (blurry lighthouse with boat) To create this lighthouse scene, the artist used organic shapes to create the

    asked by Abigail on September 14, 2017
  4. algebra

    need help with this problem can someone help me? "At the end of the week one, a stock had increased in value from $5.75 a share to $7.50 a share. Find the percent of increase at the end of week one to the nearest tenth of a

    asked by Jessica on January 28, 2010
  5. Art

    Artists make shapes in the background smaller than shapes in the foreground to communicate their distance from the viewer. How else might a landscape artist show shapes in the background to depict their distance from the viewer?

    asked by Dawn on April 14, 2015

You can view more similar questions or ask a new question.