1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleonysh [2.5K]
3 years ago
5

The length of a rectangle is 4 m less than the diagonal and the width is 5 m less than the diagonal. If the area is 82 m^2, how

long is the diagonal in meters? Round your answers to the nearest tenth.​
Mathematics
1 answer:
nikklg [1K]3 years ago
5 0

I hate rounding.

Let's call the diagonal x.  It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

x = \frac 1 2(9 \pm \sqrt{9^2-4(62)}) = \frac 1 2(9 \pm \sqrt{329})

Only the positive value makes any sense for this problem, so we conclude

x = \frac 1 2(9 \pm \sqrt{329})

That's the exact answer.  Did I mention I hate rounding?  That's about

x = 13.6 meters

Answer: 13.6

----------

It's not clear to me this problem is consistent.  By the Pythagorean Theorem the diagonal satisfies

x^2 = (x-4)^2 + (x-5)^2

which works out to

x=9 \pm 2\sqrt{10}

That's not consistent with the first answer; this problem really has no solution.  Tell your teacher to get better material.

You might be interested in
Please help me!! ......
fenix001 [56]

Answer:

b)480 cm^2

Step-by-step explanation:

perimeter=(16+12+20) cm

=48 cm

lateral surface area= perimeter × height

=48×10 =480 cm^2

4 0
3 years ago
Simplify the expression 4x+2-1/2x
oksano4ka [1.4K]

answer 41x

Step-by-step

6 0
3 years ago
Go through my questions there a surprise:)
gtnhenbr [62]

Answer:

I will do that buddy. I'll have fun

8 0
3 years ago
A student has an average of 78 on seven chapter tests. If the student's scores on six of the tests are 76, 74, 76, 80, 83, and 9
zhenek [66]

Answer:

The score is 66

Step-by-step explanation:

Say the unknown score is x

Average = Total score/no of occurrence

78 = (x + 76 + 74 + 76 + 80 + 83 + 91)/7

78 × 7 = x + 76 + 74 + 76 + 80 + 83 + 91

546 = x + 480

546 - 480 = x

66 = x

∴ x = 66

4 0
3 years ago
Solve the following formula for a<br> 4=1/3ax
OLEGan [10]
THE CORRECT ANSWER IS A=12 OVER X
4 0
3 years ago
Other questions:
  • James borrows $300 at an interest rate of 8% and takes 5 years to pay it off.
    15·2 answers
  • Find the remainder of the division of
    14·2 answers
  • carol is excited to get a new kitten from the animal shelter. the kitten had an $299 adoption fee. carol had $50 off coupon for
    12·2 answers
  • Help please help me I need this
    15·1 answer
  • Please help i’ll do anything and give the brain thing :((
    12·1 answer
  • Simplify. Evaluate the numerical bases. 2^3 x ^3y ^-2 . 2^-5 xy^2
    8·1 answer
  • Evaluate the expression when c=5 and d=7.<br><br> c+6d<br><br> Help!!!!
    11·1 answer
  • What is the value of x in the figure at the right?<br><br> 50 <br> 62<br> 68<br> 112
    8·1 answer
  • How do you write the sum of one-sixth of n and one-fifth of g
    6·1 answer
  • Lines 76-79 in Passage 2 ("The edifying . . .
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!