Question

This is a 2 part question. Need help with both questions please! Use the triangle for both parts of the question. Click on the flip picture button if needed to see pic better.

Answer 1

19. A)3cm

20. B)6.5cm

Explanation:

Given that S is the midpoint of QT and V the midpoint of QU, we can use the laws of enlargement to find the value of QR:

`QT=2QS=2ST\\\\QT=2* 9=18\\\\\\`

Using ratios:

`WV:VU=4:6=RS:ST\\\\(4)/(6)=(RS)/(9)\\\\RS=(9*4)/(6)=6`

The length of QR:

`QT=QR+RS+ST\\\\18=QR+6+9\\\\QR=3`

Hence, QR is 3cm

b. Again we use the laws of enlargement to find the value of SV :

`TQ:TS=TU:SV\\\\18:9=13:SV\\\\(18)/(9)=(13)/(SV)\\\\SV=6.5`

Hence, the length of SV is 6.5cm

Answer 2

Part A) Option A. QR= 3 cm

Part B) Option B. SV=6.5 cm

Explanation:

step 1

Find the length of segment QR

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

In this problem Triangle QRW and Triangle QSV are similar by AA Similarity Theorem

so

`(QR)/(QS)=(QW)/(QV)`

we have

`QS=9\ cm` ---> because S is the midpoint QT (QS=TS)

`QW=2\ cm` --->because V is the midpoint QU (QW+WV=VU)

`QV=6\ cm` --->because V is the midpoint QU (QV=VU)

substitute the given values

`(QR)/(9)=(2)/(6)`

solve for QR

`QR=9(2)/6=3\ cm`

step 2

Find the length side SV

we know that

The Mid-segment Theorem states that the mid-segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this mid-segment is half the length of the third side

so

In this problem

S is the mid-point side QT and V is the mid-point side QU

therefore

SV is parallel to TU

and

`SV=(1/2)TU`

so

`SV=(1/2)13=6.5\ cm`