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pentagon [3]
3 years ago
14

The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of

the trapezoid. The triangle is 2lcm base and 6cm height. decompose the triangle
Mathematics
2 answers:
Sati [7]3 years ago
8 0

Answer:

<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>

Step-by-step explanation:

The formula of an area of a triangle:

A=\dfrac{bh}{2}

<em>b</em><em> </em>- base

<em>h</em> - height

We have <em>b = 21cm, h = 6cm</em>.

Substitute:

A=\dfrac{(21)(6)}{2}=63\ cm^2

The formula of an area of a trapezoid:

A=\dfrac{b_1+b_2}{2}\cdot h

<em>b₁, b₂</em> - bases

<em>h</em><em> - </em>height

We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.

The area of a triangle and the area of a trapezoid are the same.

Therefore

\dfrac{3b_2}{2}\cdot h=63         <em>multiply both sides by 2</em>

3b_2h=126          <em>divide both sides by 3</em>

b_2h=42         <em>divide both sides by h</em>

b_2=\dfrac{42}{h}

b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}

Scrat [10]3 years ago
6 0

Answer:

The length of the bases of the trapezoid is b_1=42H and b_2=84H      

Step-by-step explanation:

Given : The triangle and the trapezoid have the same area. Base b_2 is twice the length of base b_1.

To find : What are the lengths of the bases of the trapezoid. The triangle is 21 cm base and 6 cm height decompose the triangle?

Solution :

The area of the triangle is A_t=\frac{1}{2}bh

The triangle is 21 cm base and 6 cm height,

A_t=\frac{1}{2}\times 21\times 6

A_t=63\ cm^2

The area of the trapezoid is A_T=\frac{b_1+b_2}{2}H

The triangle and the trapezoid have the same area.

i.e. 63=\frac{b_1+b_2}{2}H

Base b_2 is twice the length of base b_1

i.e. b_2=2b_1

Substitute,

63=\frac{b_1+2b_1}{2}H

63=\frac{3b_1}{2}H

126=(3b_1)H

\frac{126}{3H}=b_1

b_1=42H

Put in b_2=2b_1,

b_2=2(42H)

b_2=84H

The length of the bases of the trapezoid is b_1=42H and b_2=84H

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