MATHEMATICS HIGH SCHOOL

Find the area of ABC if the area of PRT=24 mm^2

Answers

Answer 1

Answer:

Given:

$\triangle ABC\sim\triangle PRT$

As the triangles are similar, the corresponding sides are proportional

$(AC)/(PT)=(BC)/(RT)$

Given: AC = 15, BC = 12 , PT = 6

$\begin{gathered} (15)/(6)=(12)/(RT) \n \n RT=(6\cdot12)/(15)=4.8 \end{gathered}$

We will find the area of the triangle ABC using the following ratio:

$\frac{Area\triangle\text{ABC}}{Area\triangle\text{PRT}}=(0.5\cdot AC\cdot BC\cdot\sin C)/(0.5\cdot PT\cdot RT\cdot\sin T)$

The angle C is congruent to the angle T

So, substitute with the given values:

$\begin{gathered} (Area\triangle ABC)/(24)=(15\cdot12)/(6\cdot4.8)=(180)/(28.8)=6.25 \n \n Area\triangle\text{ABC}=24\cdot6.25=150 \end{gathered}$

So, the answer will be:

The area of ΔABC = 150 mm²

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What is the length of the longer side in this triangle

Answers

Did you notice the little box with corners marked in the angle down at the bottom ?
That angle is a right angle, and this triangle is a right triangle !

This piece of information is a big help. It breaks the problem wide open.
You know that in order to find the longest side of a right triangle . . .

-- Square the length of one short side.
-- Square the length of the other short side.
-- Add the two squares together.
-- Take the square root of the sum.

One short side=48. Its square = 2,304.
The other short side=48. Its square = 2,304.
Add the two squares: 2,304 + 2,304 = 4,608

The square root of the sum = √4,608 = 67.88 (rounded)

Give me 3 examples of a ratio

Answers

Answer:

2:4 like in a basketball game 2/4 like a fraction 2:4 like a competitive thing

Step-by-step explanation:

Find the value(s) of k for which the expression is a perfect square trinomial.
49x^2-84x+k

Answers

Step-by-step explanation:

step 1. the perfect square will look like this: (7x + a)(7x + a) = (7x + a)^2.

step 2. by performing FOIL you will get 49x^2 + 14xa + a^2.

step 3. 14a = 84. a = 6

step 4. a^2 = 36.

step 5. k = 36.

A "point" is 1% of your borrowed amount on a mortgage. You want to pay 2 points to get a 0.5% reduction in your interest rate on a $175,000 mortgage. How much will you pay in points?

Answers

a point is 1% of your borrowed amount on a mortgage.
mortgage loan = 175,000

175,000 x 1% = 1,750 per point

1750 x 2 = 3,500 is the amount paid for the 2 points.

Answer: a) $3,500

Step-by-step explanation:

I got it right

Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B? a. 864 m3
b. 288 m3
c. 96 m3
d. 32 m3

Answers

The answer would be 864 m³ if the 32 volume was tripled. This is because when we are tripling the volume of the rectangle we are increasing 3 dimension, thus we will be multiplying 3 sides by the increase of which is equal to 27. Then 32 times 32 is 864 m³

Answer:

The correct option is A.

Step-by-step explanation:

It is given that the volume of box A is 32 cubic meters.

Let dimensions of the box A are l×b×h.

It is given that the dimensions of the box B were tripled than box A. So the dimensions of the box B are 3l×3b×3h.

The volume of box A is

$V=l* b* h$