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
aleksandrvk [35]
3 years ago
15

Two shapes are shown below, one isosceles triangle and one rectangle. The dimensions can be represented by algebraic expressions

, as shown in the diagram below. They both have the same area. Find the numerical value of the perimeter of the isosceles triangle. show full calculations please

Mathematics
1 answer:
liberstina [14]3 years ago
8 0

Answer:

Perimeter of Isosceles Triangle = 16 units

Step-by-step explanation:

Area of rectangle is given by the formula;

Area = 1/2 × base × height

From the diagram, base = 6x - 6 and height = 6x - 8

Thus,Area = 1/2 × (6x - 6) × (6x - 8)

Area = (3x - 3)(6x - 8) = 18x² - 42x + 24

Secondly, area of rectangle is given by;

Area = length x breadth

So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18

We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;

18x² - 42x + 24 = 18x² - 39x + 18

18x² will cancel out and rearranging, we have;

24 - 18 = 42x - 39x

6 = 3x

x = 6/3

x = 2

Plugging 2 for x for the height and base of the triangle, we have;

base = 6(2) - 6 and height = 6(2) - 8

Base = 6 and height = 4

So,let's find the slant height of the isosceles triangle.

Dividing the base by 2,we have; 6/2 = 3

So,using Pythagoras theorem, let the slant height be h, so we have;

h² = 3² + 4²

h² = 9 + 16

h² = 25

h = √25

h = 5

2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units

You might be interested in
Solve for x. x÷(-2)=1.4​
nignag [31]

Answer:

x=-2.8

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please help me with this and fast!
Serjik [45]

Answer:

16

5

O

I think

Step-by-step explanation:

7 0
3 years ago
Please help me Im almost done​
SSSSS [86.1K]

Answer:

\mathsf {x = 76}

Step-by-step explanation:

The given pair of angles lie on a line, hence they are classified as linear angles. They possess the property by which their sum is equal to 180°.

\textsf {Solving :}

\implies \mathsf {x + 17 + 87 = 180}

\implies \mathsf {x + 104 = 180}

\implies \mathsf {x = 180 - 104}

\implies \mathsf {x = 76}

8 0
2 years ago
Which relation is a function
Alla [95]
Every x value should have only one value of y.
So the answer is the last choice.
8 0
3 years ago
Read 2 more answers
Jacob walks 1.5 miles north. He turns and walks 0.8 miles west. How far is he from his starting point?
Flura [38]

Answer:

1.7 miles

Step-by-step explanation:

Given that,

Jacob walks 1.5 miles north.

He turns and walks 0.8 miles west.

We need to find how far is he from his starting point. Let he is at a distance of x miles from the starting point. It can be calculated as follows :

x=\sqrt{1.5^2+0.8^2} \\\\x=1.7\ \text{miles}

Hence, he is 1.7 miles from his starting point.

7 0
2 years ago
Other questions:
  • Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20 degrees and angel BCA measures 30 degree
    14·1 answer
  • How much paper is used for the label on the can of peas? Round your answer to the nearest tenth of a square inch.
    6·1 answer
  • Find three solutions of the equation (x^2-9)(x^3-8)=0
    12·1 answer
  • Write the expression in factored form.<br> m²-nt
    12·1 answer
  • Choose the function
    7·1 answer
  • the area of a projected picture on a movie screen varies directly as the square of the distance from the projector to the screen
    8·1 answer
  • Hi please someone give me the algebraic expression to this question.
    13·1 answer
  • PLEAWSE HELP GIVING BRAINLIEST!!!<br> PLEASEEEEEEEee
    13·1 answer
  • Can anyone help me with this math equation plsss?
    7·1 answer
  • What is the EXPLICIT equation for 3, 6, 12, 24...?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!