Mathematics

Question

Can anyone give a step-by-step guide on how to answer these types of questions? I'm really struggling with similar shapes so thank you in advance.
Can anyone give a step-by-step guide on how to answer these types of questions? I'm really struggling with similar shapes so thank you in advance.

2 Answer

  • Answer:

    a) 8cm

    b) 19.8cm

    Step-by-step explanation:

    The key to these types of questions is to keep proportions in mind.

    To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.

    The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.

    CD = 4.8 * (10/6) = 8

    CD = 8cm

    For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.

    AC = 4.5 * (10/6) = 7.5

    AC = 7.5

    But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.

    7.5 - 4.5 = 3

    So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.

    4.8 + 4 + 8 + 3 = 19.8cm.

    Hope this helps.

  • Answer:

    a) CD = 8 cm

    b) Perimeter of EBCD is 19.8 centimeters

    Step-by-step explanation:

    For this question, you can assume that ΔABE and ΔACD are similar. That's proven by BE ║ CD, but that's not directly relevant to the question so I won't explain it unless you would like me to.

    In 2 similar triangles, all corresponding angles are congruent and all corresponding sides have the same scale factor.

    For example, in ΔABC and ΔXYZ:

    [tex]\frac{AB}{XY} =\frac{AC}{XZ} =\frac{BC}{YZ}[/tex]

    Using those relationships, you can solve for any side in one triangle given the corresponding side in the other triangle.

    A)

    In the given triangles ΔABE and ΔACD, CD corresponds to BE, so:

    [tex]\frac{CD}{BE} =\frac{AD}{AE}[/tex]

    where AD is just 6 + 4 = 10.

    [tex]\frac{CD}{4.8} =\frac{10}{6} \\\\\frac{CD}{4.8} =1.6667\\\\CD=8[/tex]

    CD = 8cm

    B)

    Doing the same thing as above, now find the length of AC:

    [tex]\frac{AC}{AB} =\frac{AD}{AE} \\\\\frac{AC}{4.5} =\frac{10}{6}\\\\\frac{AC}{4.5} =1.6667\\\\AC=7.5[/tex]

    Now, to find BC:

    [tex]BC=AC-AB\\BC=7.5-4.5\\BC=3[/tex]

    Finally, add up the sides to find the perimeter of EBCD:

    [tex]4.8+3+8+4\\19.8[/tex]

    Perimeter of EBCD is 19.8 centimeters

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