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3 years ago

Help me please I need it

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

Answer:

width = 8 feet and length = 12 feet

Step-by-step explanation:

Let the width be w then the length = 3w - 12 ( 12 less than 3 times the width )

The area (A) of a rectangle is

A = length × width, that is

w(3w - 12) = 96 ← area of floor

3w² - 12w = 96 ( subtract 96 from both sides )

3w² - 12w - 96 = 0 ← in standard form for a quadratic equation

Divide all terms by 3

w² - 4w - 32 = 0

Consider the product of the factors of the constant term ( - 32) which sum to give the coefficient of the w- term (- 4)

The factors are - 8 and + 4, since

- 8 × 4 = - 32 and - 8 + 4 = - 4, hence

(w - 8)(w + 4) = 0

Equate each factor to zero and solve for w

w - 8 = 0 ⇒ w = 8

w + 4 = 0 ⇒ w = - 4

However, w > 0 ⇒ w = 8

Hence width = 8 feet

length = 3w - 12 = (3 × 8) - 12 = 24 - 12 = 12 feet

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Answer:

x=3.89

Step-by-step explanation:

I'll go in depth for you.

Before we figure out what we do, let understand what we know about this triangle.

We know that both triangles have a angle that measure 27°.
We also know EH=5
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ZG=7
We need to know how to find EZ

Notice how line EG and HF intersect at Angle Z. We know that if two lines intersect at an angle, it form angles called vertical angles. This means that the two angles that are vertical to each other are congruent.

This means that angle Z in both triangles both measure the same.

Now since both triangles have 2 congruent corresponding angles, we can say that the Triangles are Similar due to the Angle-Angle Postulate.

"If two corresponding angles of two triangles are congruent, then the two triangles are similar."

What is mean when Triangles are similar? 

It means that the similar triangles corresponding angles are equal and their sides are in proportion.

The corresponding sides are 

EH and GF

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Our proportion formula for similar triangles is 

Any two sides of the first triangle divided by each other must equal the two corresponding sides of the second triangles divided by each other respectively.