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DaniilM [7]
3 years ago
14

The altitude of a triangle is 2 m longer than its base. What are the dimensions of the altitude and the base if thearea of the t

riangle is 40 m^2?
Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Step-by-step explanation:

Let base of triangle be x m.

Therefore, altitude =( x + 2)m

area \: of \:  \triangle =  \frac{1}{2}  \times base \times altitude \\  \\ 40 =  \frac{1}{2}  \times x \times (x + 2) \\  \\ 80 =  {x }^{2} +2x \\  \\   {x}^{2}  + 2x - 80 = 0 \\  {x}^{2}  + 10x - 8x - 80 \\ x(x + 10) - 8(x + 10)  = 0\\ (x + 10)(x - 8) = 0 \\ x + 10 = 0 \:  \: or \:  \: x - 8 = 0 \\ x =  - 10 \:  \: or \:  \: x = 8 \\ base \: can \: not \: be \:  - ve \\ x \neq - 10 \\ x = 8 \\ x + 2 = 8 + 2 = 10 \\

Therefore

Altitude = 10 m

Base = 8 m

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Zigmanuir [339]

Answer:

m(∠C) = 18°

Step-by-step explanation:

From the picture attached,

m(arc BD) = 20°

m(arc DE) = 104°

Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.

m(∠C) = \frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}]

Since, AB is a diameter,

m(arc BD) + m(arc DE) + m(arc EA) = 180°

20° + 104° + m(arc EA) = 180°

124° + m(arc EA) = 180°

m(arc EA) = 56°

Therefore, m(∠C) = \frac{1}{2}(56^{\circ}-20^{\circ})

m(∠C) = 18°

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Answer:

(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

Step-by-step explanation:

We proceed to solve algebraically and explain each step:

1) 4\cdot x +1 +x + 3 = -11 GIven

2) 4\cdot x +x +1 + 3 = -11 Commutative property

3) (4+1)\cdot x +4 = -11 Distributive property/Definition of addition

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8) x = - 3 Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

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(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

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