GEOMETRY: PLEASE HELP!!

Mathematics

1 answer:

Aloiza [94]3 years ago

7 0

Answer:

$GF=72$

Step-by-step explanation:

All triangles in the given figure are similar, from SAS. Notice that marked in the diagram, $CD=DE=EF=FA$ .

For triangle $\triangle CGF$ was base $GF$ , leg $CF$ contains three of these marked segments. In triangle $\triangle CHE$ with base $HE$ , leg $CE$ has two of these marked segments. By definition, similar polygons have corresponding sides in a constant proportion. Therefore, the length of GF must be $3/2$ the length of EH. Since the length of EH is given as 48, we have:

$GF=\frac{3}{2}EH, \\\\GF=\frac{3}{2}\cdot 48,\\\\GF=\boxed{72}$

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The perimeter of the patio is 64 feet. The width of the patio is (x+2) feet and the length of the patio is (x+6) feet. What are

ValentinkaMS [17]

The formula for the perimeter is P = 2w + 2l, where w is the width and l is the length. It is given that the width = (x+2) and the length = (x+6). Therefore, we can make this equation:

P = 2w + 2l

64 = 2(x+2) + 2(x+6) ⇒ Distributive property

⇒ 64 = 2x + 4 + 2x + 12 ⇒ Combine like terms

⇒ 64 = 4x + 16 ⇒ Subtract 16 from both sides

⇒ 48 = 4x ⇒ Divide both sides by 4

⇒ x = 12

Then, we use x = 12 and substitute it in to find the length and width

Width = (x+2) = (12+2) = 14

Length = (x+6) = (12+6) = 18

The dimensions of the patio is 14 by 18

5 0

3 years ago