Exercise 12 Page 451

We know the height of two equal prisms but all the sides of only 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 b, c, and h one at a time.

Finding b

We know that a prism with a height of 5 meters and a side of 12 meters is similar to a prism with a height of 7.5 meters and a side of b. We can use this information to write a proportion. Height of bigger prism/Height of smaller prism = Side of bigger prism/Side of smaller prism Let's substitute the corresponding dimensions into this equation and solve for b.

Height of bigger prism/Height of smaller prism=Side of bigger prism/Side of smaller prism

SubstituteValues

Substitute values

7.5/5=b/12

▼

Solve for b

MultEqn

LHS * 12=RHS* 12

7.5/5 * 12=b

MoveRightFacToNum

a/c* b = a* b/c

7.5 * 12/5=b

Multiply

Multiply

90/5=b

CalcQuot

Calculate quotient

18=b

RearrangeEqn

Rearrange equation

b=18

The length of the prism b is 18 meters long.

Finding c

We know that a prism with a height of 5 meters and a side of 13 meters is similar to a prism with a height of 7.5 meters and a side of c. We can use this information to write a proportion. Height of bigger prism/Height of smaller prism = Side of bigger prism/Side of smaller prism Let's substitute the corresponding dimensions into this equation and solve for c.

Height of bigger prism/Height of smaller prism=Side of bigger prism/Side of smaller prism

SubstituteValues

Substitute values

7.5/5=c/13

▼

Solve for c

MultEqn

LHS * 13=RHS* 13

7.5/5 * 13=c

MoveRightFacToNum

a/c* b = a* b/c

7.5 * 13/5=c

Multiply

Multiply

97.5/5=c

CalcQuot

Calculate quotient

19.5=c

RearrangeEqn

Rearrange equation

c=19.5

The length of the prism c is 19.5 meters long.

Finding h

We know that a prism with a height of 5 meters and a side of 6 meters is similar to a prisms with a height of 7.5 meters and a side of h. We can use this information to write a proportion. Height of bigger prism/Height of smaller prism = Side of bigger prism/Side of smaller prism Let's substitute the corresponding dimensions into this equation and solve for h.

Height of bigger prism/Height of smaller prism=Side of bigger prism/Side of smaller prism

SubstituteValues

Substitute values

7.5/5=h/6

▼

Solve for h

MultEqn

LHS * 6=RHS* 6

7.5/5 * 6=h

MoveRightFacToNum

a/c* b = a* b/c

7.5 * 6/5=h

Multiply

Multiply

45/5=h

CalcQuot

Calculate quotient

9=h

RearrangeEqn

Rearrange equation

h=9

The length of the prism h is 9 meters long.