Question

To the nearest tenth, what is the length of QR

Answer 1

`\displaystyle B )\overline{ \text{QR }}= 17.6 cm`

Explanation:

we have two similar triangles

we want to figure out the measure of QR

remember that,

the ratio of the corresponding sides of two similar triangles is equal

thus,

`\displaystyle (8 .8)/(QR) = (5.2)/(10.4)`

cross multiplication:

`\displaystyle5.2 QR = 91.52`

divide both sides by 5.2:

`\displaystyle (5.2 QR )/(5.2)= ( 9 1.52)/(5.2)`

simplify division:

`\displaystyle QR = 17.6 cm`

hence, our answer is B

Answer 2

|QR| = 17.6

Explanation:

To answer this we need to show that the triangles are similar or to assume that they are similar.

Note the following:

1. The ratio of the longest sides is 12.5 to 25.0, or 1/2;

2. The ratio of the shortest sides is 5.2 to 10.4, or 1/2

Therefore the ratio of the longer legs is 8.8 to QR, also equal to 1/2

8.8 1

-------- = -----

QR 2

Cross-multiplying, we get |QR| = 17.6