We know the height of two similar prisms but the length and width of just one of them.

Similar solids are solids that have the same shape and proportional corresponding dimensions. Therefore, the ratio between corresponding dimensions is constant. We can use this information to find the values of $ℓ$ and $w$ one at a time.

Finding $ℓ$

We know that a prism with a height of

20

inches and a length of

11

inches is similar to a prism with a height of

8

inches and a length of

ℓ

inches. We can use this information to write a proportion.

\frac{Height of bigger prism}{Height of smaller prism} = \frac{Length of bigger prism}{Length of smaller prism}

Let's substitute the corresponding dimensions into this equation and solve for

ℓ .

\frac{Height of bigger prism}{Height of smaller prism} = \frac{Length of bigger prism}{Length of smaller prism}

SubstituteValues

Substitute values

\frac{2 0}{8} = \frac{1 1}{ℓ}

▼

Solve for

ℓ

MultEqn

$LHS \cdot ℓ = RHS \cdot ℓ$

\frac{2 0}{8} \cdot ℓ = 11

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

\frac{2 0 ℓ}{8} = 11

MultEqn

$LHS \cdot 8 = RHS \cdot 8$

20 ℓ = 11 \cdot 8

Multiply

20 ℓ = 88

DivEqn

$LHS / 20 = RHS / 20$

ℓ = \frac{8 8}{2 0}

CalcQuot

Calculate quotient

ℓ = 4.4

The length of the prism

ℓ

is

4.4

inches long.

Finding $w$

We know that a prism with a height of

20

inches and a width of

8

inches is similar to a prism with a height of

8

inches and a width of

w

inches. We can use this information to write a proportion.

\frac{Height of bigger prism}{Height of smaller prism} = \frac{Width of bigger prism}{Width of smaller prism}

Let's substitute the corresponding dimensions into this equation and solve for

w .

\frac{Height of bigger prism}{Height of smaller prism} = \frac{Width of bigger prism}{Width of smaller prism}

SubstituteValues

Substitute values

\frac{2 0}{8} = \frac{8}{w}

▼

Solve for

w

MultEqn

$LHS \cdot w = RHS \cdot w$

\frac{2 0}{8} \cdot w = 8

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

\frac{2 0 w}{8} = 8

MultEqn

$LHS \cdot 8 = RHS \cdot 8$

20 w = 8 \cdot 8

Multiply

20 w = 64

DivEqn

$LHS / 20 = RHS / 20$

w = \frac{6 4}{2 0}

CalcQuot

Calculate quotient

w = 3.2

The width of the prism

w

is

3.2

inches long.

Finding ℓ

Finding w

Finding $ℓ$

Finding $w$

Exercise