Express the area of the entire rectangle. ?

Mathematics

2 answers:

marshall27 [118]3 years ago

8 0

Answer:

x² + 9x + 20

Step-by-step explanation:

Area of a rectangle can be found by multiplying the base with height (or length with width).

A(r) = l x h.

Multiply. Plug in:

x + 5 for l

x + 4 for h

A(r) = (x +5) * (x + 4)

Use the FOIL method to solve. Multiply the first terms of both parenthesis, the outside terms, the inside terms, and then the last terms. Combine like terms:

A(r) = (x + 5) * (x + 4)

x * x = x²

x * 4 = 4x

5 * x = 5x

4 * 5 = 20

x² + 4x + 5x + 20

x² + (4x + 5x) + 20

x² + 9x + 20

x² + 9x + 20 is your answer.

ser-zykov [4K]3 years ago

6 0

(x+4)(x+5)

x^2 + 5x + 4x + 20

x^2 + 9x + 20

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The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the mi

lakkis [162]

Answer:

∠TAC is approximately equal to 61.6°

Step-by-step explanation:

The given parameters for the pyramid are;

The dimension for the rectangular base are; Length = 9 cm, width = 7 cm

The length of the diagonal sides, TA, TB, TC, and TD = 12 cm each

The midpoint of the rectangular base = Point M

The diagonal AC = AM + MC

AM = MC as given M is the midpoint of the rectangular base

∴ AC = AM + MC = 2·AM

By Pythagoras' theorem, AC = √(9² + 7²) = √130

AC = √130 cm

∴ AM = AC/2 = (√130)/2 cm

Alternatively, AM = √((9/2 cm)² + (7/2 cm)²) = √(32.5) cm

∠TAC = ∠TAM

By trigonometric ratios, we have;

$cos (\theta) = \dfrac{Length \ of \ adjacent \ side \ to \ angle }{Length \ of \ hypotenuse\ side \ to \ angle}$

$\therefore cos (\angle TAM) = cos (\angle TAC) = \dfrac{\left (\dfrac{\sqrt{130} }{2} \right )}{12} = \dfrac{\sqrt{130} }{2 \times 12} = \dfrac{\sqrt{130} }{24}$