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Anna11 [10]
2 years ago
10

Triangles A and B have vertical heights x cm and (x+3) cm respectively. The areas of Triangles A and B are 30cm² and 32cm² respe

ctively. (a) Find, in terms of x, an expression for the base of: (i) Triangle A (ii) Triangle B (b) Given that the base of Triangle B is 4 cm less than the base of Triangle A, form an equation and show that it reduces to x² + 4x - 25 = 0 (c) Solve the equation and hence, find the height of Triangle B.​
Mathematics
1 answer:
PolarNik [594]2 years ago
3 0

Answer:

Hi,

Step-by-step explanation:

Let say a the base of the triangle A and b the base of the triangle B.

a)\\\left\{\begin{array}{ccc}\dfrac{a*x}{2}&=&30\\\dfrac{b*(x+3)}{2}&=&32\\b=a-4\\\end{arraqy}\right.\\\\(i): a=\dfrac{60}{x}\\\\(ii): b=\dfrac{64}{x+3}\\\\b)\\\dfrac{64}{x+3}=\dfrac{60}{x}-4\\\\64x=(60-4x)*(x+3)\\\\4x^2+16x-180=0\\\\x^2+4x-45=0\\\\\Delta=16+4*45=196=14^2\\x=\dfrac{-4+14}{2}=5\ or\ x=\dfrac{-4-14}{2}=-9\ (impossible)\\So\ x=5,\ a=\dfrac{60}{5}=12, b=\dfrac{64}{5+3}=8\\\\Area\ of\ A=12*5/2=30\\Area\ of\ B=8*8/2=32\\\\Height\ of\ triangle\ B=x+3=5+3=8.\\

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DiKsa [7]

Answer:

27in, 36in, 45in

Step-by-step explanation:

a = 27 \\ b = 36 \\ c = 45

{c}^{2} =  {a}^{2}  +  {b}^{2}

c = \sqrt{ {a}^{2} +  {b}^{2}  }

45{ = }^{?}   \sqrt{ {27}^{2} +  {36}^{2}  }

45  { = }^{?}   \sqrt{729 + 1296}

45  { = }^{?}   \sqrt{2025}

45 = 45

6 0
3 years ago
A triangle has sides with lengths of 45 feet, 76 feet, and 90 feet. Is it a right triangle?
Marat540 [252]

Answer:

No

Step-by-step explanation:

6 0
3 years ago
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The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary sch
VARVARA [1.3K]

Answer:

90 bags of sand

Step-by-step explanation:

9 feet × 1.5 = 13.5

12 feet × 1.5 = 18

Large pit area= 13.5 × 18 = 243ft squared

The small pit area=9 × 12 = 108ft squared

243 / 108 = 2.25 times larger

This means the large pit needs 2.25 times more sand.

40 × 2.25 = 90 bags of sand

5 0
4 years ago
Read 2 more answers
Please solve this question asap
disa [49]

Step-by-step explanation:

y =  \sqrt{4x + 6}

{y}^{2}  = 4x + 6

{y}^{2}  - 6 = 4x

\frac{1}{4} ( {y}^{2}  - 6) = x

Swap x and y

\frac{ {x}^{2} - 6 }{4}  = y

3 0
2 years ago
Substitute x+2y=8 3x+2y=6
vekshin1
Use x+2y=8
Subtract 2y to make
x=8-2y

Plug this in to the other equation
3(8-2y)+2y=6

Distribute the 3
24-6y+2y=6

Combine like terms
24-4y=6

Solve
18/4=y, 9/2=y

Plug and solve for x
X+2y=8
X+(2*9/2)=8
X+9=8
X=-1
8 0
3 years ago
Read 2 more answers
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