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Triangle PQR is similar to Triangle P'Q'R' as shown in the diagrams below. (i) Find the scale factor of enlargement from Triangle PQR to Triangle P'Q'R'. (ii) Find the length of P'Q. (iii) Find the length of P'R.

Mathematics

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Answers

3 parts
a

3\text{3}

b

15 cm\text{15 cm}

c

3 cm\text{3 cm}

Step-by-step solution

9 steps

Haya, twende na swali hili la pembetatu zinazofanana.

Part a· 3 steps

Ili kupata kipimo cha ukuzaji (scale factor) kutoka Pembetatu PQR kwenda Pembetatu P'Q'R', tunagawanya urefu wa upande unaolingana wa Pembetatu P'Q'R' kwa urefu wa upande wa Pembetatu PQR.

  1. Tambua pande zinazolingana zenye vipimo vilivyotolewa.

    Upande QR wa Pembetatu PQR una urefu wa 4 cm4 \text{ cm}.
    Upande Q'R' wa Pembetatu P'Q'R' una urefu wa 12 cm12 \text{ cm}.
    Hizi ni pande zinazolingana.

  2. Kokotoa kipimo cha ukuzaji.

    Kipimo cha ukuzaji=Urefu wa Q’R’Urefu wa QR=12 cm4 cm\text{Kipimo cha ukuzaji} = \frac{\text{Urefu wa Q'R'}}{\text{Urefu wa QR}} = \frac{12 \text{ cm}}{4 \text{ cm}}

  3. Rahisisha.

    Kipimo cha ukuzaji=3\text{Kipimo cha ukuzaji} = 3

    Kipimo cha ukuzaji ni 3\boxed{\text{3}}.

Part b

15 cm\text{15 cm}

Ili kupata urefu wa P'Q', tunatumia kipimo cha ukuzaji tulichopata na urefu wa upande unaolingana wa Pembetatu PQR.

  1. Tambua urefu wa upande PQ.

    Urefu wa PQ ni 5 cm5 \text{ cm}.

  2. Tumia kipimo cha ukuzaji kukokotoa urefu wa P'Q'.

    Urefu wa P’Q’=Kipimo cha ukuzaji×Urefu wa PQ\text{Urefu wa P'Q'} = \text{Kipimo cha ukuzaji} \times \text{Urefu wa PQ} Urefu wa P’Q’=3×5 cm\text{Urefu wa P'Q'} = 3 \times 5 \text{ cm}

  3. Kokotoa thamani.

    Urefu wa P’Q’=15 cm\text{Urefu wa P'Q'} = 15 \text{ cm}

    Urefu wa P'Q' ni 15 cm\boxed{\text{15 cm}}.

Part c

3 cm\text{3 cm}

Ili kupata urefu wa PR, tunatumia urefu wa upande unaolingana wa Pembetatu P'Q'R' na kipimo cha ukuzaji.

  1. Tambua urefu wa upande P'R'.

    Urefu wa P'R' ni 9 cm9 \text{ cm}.

  2. Tumia kipimo cha ukuzaji kukokotoa urefu wa PR.

    Urefu wa PR=Urefu wa P’R’Kipimo cha ukuzaji\text{Urefu wa PR} = \frac{\text{Urefu wa P'R'}}{\text{Kipimo cha ukuzaji}} Urefu wa PR=9 cm3\text{Urefu wa PR} = \frac{9 \text{ cm}}{3}

  3. Kokotoa thamani.

    Urefu wa PR=3 cm\text{Urefu wa PR} = 3 \text{ cm}

    Urefu wa PR ni 3 cm\boxed{\text{3 cm}}.

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