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

Question

3 years ago

13

bases of the trapezoid?

2 answers:

gulaghasi [49] · Answer 1 · 2022-03-29T15:27:25+03:00

Answer: b₁ = 7 and b₂ = 14.

Triangle: base=21 cm, height=6cm

Trapezoid: height=6 cm, b1=?, b2=?

Triangle -> A=bh/2 -> A=63 (<em>b is base and h is height)</em>

Trapezoid -> A=[(b₁+b₂)/2)]h (<em>b₁ and b₂ are bases and h is height)</em>

Since they have the same area, the formula will be:

63=[(b₁+2(b₁))/2)]h

x=7

GaryK [48] · Answer 2 · 2022-03-29T17:34:47+03:00

Answer:

b₁ = 7 cm, b₂ = 14 cm

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

Here b = 21 and h = 6, then

A = 0.5 × 21 × 6 = 63 cm²

The area (A) of a trapezoid is calculated as

A = $\frac{1}{2}$ h (b₁ + b₂ )

Here A = 63 ( same as triangle ), h = 6 and b₂ = 2b₁ , then

0.5 × 6 × (b₁ + 2b₁ ) = 63

3 × 3b₁ = 63

9b₁ = 63 ( divide both sides by 9 )

b₁ = 7

and b₂ = 2 × 7 = 14

The bases of the trapezoid are 7 cm and 14 cm