The volume of a Rectangular Prism

Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy

Darina [25.2K]

Answer:

12 m

Step-by-step explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

$\frac{AD}{EH} = \frac{2}{3}$

$\frac{8}{EH} = \frac{2}{3}$

Cross multiply

$3*8 = 2*EH$

$24 = 2*EH$

Divide both sides by 2 to make EH the subject of formula

$\frac{24}{2} = \frac{2*EH}{2}$

$12 = EH$

The length of side EH = 12 m

5 0

3 years ago

Plz explain and prove the triangles congruence.

ziro4ka [17]

Answer:

The explanation is given below with the diagram.

Step-by-step explanation:

Given:

Δ ABC is an Isosceles triangle with base AB.

D is the midpoint of AB

∴ AD = BD

To Prove:

$\angle ACD \cong \angle BCD$

Proof:

Isosceles triangle property:

If Δ ABC is an Isosceles triangle with base AB, then the two sides are congruent and the base angles are congruent.

$\therefore \overline{AC} \cong \overline {BC}\ and\\\therefore \angle CAD} \cong \angle CBD$

$In\ \triangle ACD\ and\ \triangle BCD\\\overline{AC} \cong \overline{BC}\ \textrm{ Two sides of Isosceles Triangle are congruent}\\\angle CAD \cong \angle CBD\ \textrm{Base angles of Isosceles Triangle are congruent }\\\overline{AD} \cong \overline{BD}\ \textrm{ D is the midpoint of AB given}\\\therefore \triangle ACD \cong \triangle BCD\ \textrm{ By Side-Angle-Side test}\\\therefore \angle ACD \cong \angle BCD\ \textrm{corresponding parts(angles) of congruent triangles}\\$

$\therefore \angle ACD \cong \angle BCD\ \textrm{ Proved}$

7 0

3 years ago

If x +13/3 =5 what is x?

sesenic [268]

Answer:

.66

Step-by-step explanation:

8 0

3 years ago

How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one q

Paraphin [41]

Answer:

Total distance traveled= 21h miles

Step-by-step explanation:

You biked at 10 mph for h hours

Speed= 10 mpg

Time = h hours

Distance covered= speed*time

Distance covered= 10h miles

walked at 3mph for twice as long as I biked,

Speed= 3 mph

Time= twice as long as biked

Time= 2(h) hours

Distance= 2h*3

Distance= 6h miles

ran at 10mph for one quarter as long as I walked

Speed= 10 mph

Time= 1/4 of(2h)

Time= 1/2h hours

Distance= 1/2h*10

Distance= 5h miles

Total distance traveled

= 10h miles +6h miles+ 5h miles

Total distance traveled= 21h miles

6 0

3 years ago

Help me please just with one question

Snowcat [4.5K]

Given:

Composite figure made of cylinder and two spheres.

To find:

The volume of the composite solid.

Solution:

Radius = 2 in

The value of π = 3.14

<u>Volume of sphere:</u>

$$V=\frac{4}{3} \pi r^3$

$$V=\frac{4}{3} \times 3.14 \times 2^3$

$$V=\frac{4}{3} \times 3.14 \times 8$

$V=33.49$

Volume of a sphere is 33.49 in³

Volume of two spheres = 2 × 33.49 = 66.98 in³

Radius of cylinder = 2 in

Height of cylinder = 8 - 2 - 2 = 4 in

<u>Volume of cylinder:</u>

$$V=\pi r^2 h$

V = 3.14 × 2² × 4

V = 50.24

Volume of cylinder = 50.24 in³

Volume of composite solid = Volume of two spheres + Volume of cylinder

= 66.98 in³ + 50.24 in³

= 117.2 in³

The volume of the composite solid is 117.2 in³.

6 0

3 years ago