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katen-ka-za [31]
3 years ago
14

The height of a trapezoid is 1/4 the sum of the lengths of its bases. The height is 2 1/2 feet. Find the area if the trapezoid.

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

Step-by-step explanation:

(1/4)*sum of lengths of bases = Height of trapezoid

(1/4)*(a + b) = 2 1/2

\frac{1}{4}*(a+b)=\frac{5}{2}\\\\a+b=\frac{5}{2}*\frac{4}{1}\\\\a+b=5*2\\\\a+b=10

Area=\frac{(a+b)*h}{2}\\\\=\frac{10*\frac{5}{2}}{2}\\\\=\frac{5*5}{2}\\\\=\frac{25}{2}

= 12.5 ft²

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3 years ago
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3 years ago
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2
Oksanka [162]

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

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By Zero Product property, either x=0

or, x-11=0

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So, Width=x/10=11/10=1.1

Checking:

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Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

7 0
3 years ago
Read 2 more answers
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