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Luba_88 [7]
3 years ago
5

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

of the triangle DBC.

Mathematics
1 answer:
Ivan3 years ago
4 0
Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}

The base x is 4, the height h is 3/5. Calculate the area:

A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}

The area of triangle DBC is 6/5.

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MatroZZZ [7]

Answer:

\frac{x^3-a^3}{0}

Step-by-step explanation:

\frac{x^4-a^4}{x-a}

divide by x-a

\frac{x^3-a^3}{0}

3 0
3 years ago
Is triangle MNL congruent to triangle QNL? Why or why not? Yes, they are congruent by either ASA or AAS. Yes, they are both righ
sergij07 [2.7K]
See the attached figure which represent the rest of the question.
The rest of the question is the attached figure.
==============================================
As shown in the attached figure:
(1) ΔMNL is a right triangle at ∠MNL and ∠NML = 58°
∴ ∠L = 180° - (90°+58°) = 32°

(2) ΔQNL is a right triangle at ∠QNL and ∠QLN = 32°
∴ ∠Q = 180° - (90°+32°) = 58°

So, for both of ΔMNL and ΔQNL
1.  ∠NLM = ∠ NLQ = 32°
2.  ∠Q = ∠M = 58°
3.  side NL = side NL
∴ ΔMNL is congruent to ΔQNL by AAS

=======OR=======

So, for both of ΔMNL and ΔQNL
1.  ∠MNL = ∠QNL  = 90°
2.  side NL = side NL
3.  ∠NLM = ∠ NLQ = 32°
∴ ΔMNL is congruent to ΔQNL by ASA

=====================================
So, the correct answer is the first option

Yes, they are congruent by either ASA or AAS




3 0
3 years ago
Read 2 more answers
Can someone please help me this?<br> Math 8
Viefleur [7K]

Answer:

5x + ( - 8)x + 9 + ( - 4) \\ 5x - 8x + 9 - 4 \\  - 3x + 5

this is the solution

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Your answer is 1,631. Thanks (;
8 0
3 years ago
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solve this word problem leading to quadratic equation: the area of a rectangle is 60cm². The length is 11cm more than the width.
morpeh [17]

Answer:

Step-by-step explanation:

let : x The length and y the width you have this system :

xy =60....(1)

x = y+10...(2)

put the value for x in (1):  (y+10)y =60

the quadratic equation is : y² +10y - 60 = 0

Δ =b² - 4ac        a = 1        b= 10      c= - 60

Δ =10² - 4(1)(-60) = 324 =18²

y 1 = (-10-18)/2 negatif...... refused

y 2 = (-10+18)/2 =4

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8 0
3 years ago
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