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Debora [2.8K]
3 years ago
13

The corresponding sides of abc and def have equal lengths. the area of abc is 4 square units, and the longest side of def is 5 u

nits long. What is the area of def
Mathematics
2 answers:
seropon [69]3 years ago
7 0

Answer:

4 units

Step-by-step explanation:

borishaifa [10]3 years ago
3 0
1. "<span>The corresponding sides of (triangles) abc and def have equal lengths.</span>" means that the triangles are congruent, that is exactly identical, by the Side Side Side (SSS) postulate.

2. 2 congruent triangle, have equal area

3. A(DEF)=A(ABC)=4 square units

Answer: 4 units squared
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Please show working out thanks
IgorLugansk [536]

Answer:

10m x 15m

Step-by-step explanation:

You are given some information.

1. The area of the garden: A₁ = 150m²

2. The area of the path: A₂ = 186m²

3. The width of the path: 3m

If the garden has width w and length l, the area of the garden is:

(1) A₁ = l * w

The area of the path is given by:

(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36

Multiplying (2) with l gives:

(3) A₂l = 6l² + 6lw + 36l

Replacing l*w in (3) with A₁ from (1):

(4) A₂l = 6l² + 6A₁ + 36l

Combining:

(5) 6l² + (36 - A₂)l +6A₁ = 0

Simplifying:

(6) l² - 25l + 150 = 0

This equation can be factored:

(7) (l - 10)*(l - 15) = 0

Solving for l we get 2 solutions:

l₁ = 10, l₂ = 15

Using (1) to find w:

w₁ = 15, w₂ = 10

The two solutions are equivalent. The garden has dimensions 10m and 15m.

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3 years ago
The top of a table is in the shape of a trapezoid. It has a height 1.5 feet and the two parallel bases measure 3 feet and 5 feet
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Area = (3+5)/2 x 1.5

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Answer:

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