Question

I need help with this question.

Answer 1

See below ~

Explanation:

Let the bases be x and x + 6.

Substituting the known values into the formula :

• A = 1/2 x (a + b) x h
• 48 = 1/2 x (x + x + 6) x 4
• 2x + 6 = 24
• 2x = 18
• x = 9

The base lengths are :

1. x = 9 inches
2. x + 6 = 9 + 6 = 15 inches

Answer 2

One base is
`\large \boxed{\sf 9}` inches for one of the bases and
`\large \boxed{\sf 15}` inches for the other base.

`\large \boxed{\sf 24}=\sf(b_1+b_2)`. Use guess and check to find two numbers that add to
`\large \boxed{\sf 24}` with one number 6 more than the other to get

`\large \boxed{\sf 9}` inches for one of the bases and
`\large \boxed{\sf 15}` inches for the other base.

Explanation:

`\textsf{Area of a trapezoid}= \sf (1)/(2)(b_1+b_2)h \quad \textsf{(where b are the bases and h is the height)}`

Given:

• Area = 48 in²
• h = 4 in

Substitute given values into the formula to find (b₁ + b₂) :

`\implies \sf 48=(1)/(2)(b_1+b_2)4`

`\implies \sf (48)/(4)=(1)/(2)(b_1+b_2)`

`\implies \sf 12=(1)/(2)(b_1+b_2)`

`\implies \sf 12 \cdot 2=(b_1+b_2)`

`\implies \sf 24=(b_1+b_2)`

Therefore:

`\large \boxed{\sf 24}=\sf(b_1+b_2)`

Let:

• Base b₁ = x in
• Base b₂ = (x + 6) in

`\implies \sf (b_1+b_2)=24`

`\implies \sf x+x+6=24`

`\implies \sf 2x+6=24`

`\implies \sf 2x=18`

`\implies \sf x=9`

`\sf If\:b_1=9\:in,\:then\:b_2=9+6=15\:in`

Therefore,

• Base b₁ = 9 in
• Base b₂ = 15 in