Question

7. Triangle LMN is similar to triangle OPR. Find PR.

Answer 1

x = 101.8

Explanation:

To find:-

• The length of PR .

Answer:-

We are here given that ∆LMN is similar to ∆OPR. When triangles are similar,their ratio of corresponding sides are proportional.

So , here we have;

`\sf:\implies (NL)/(NM)=(RO)/(RP)\\`

As in the two triangles side corresponding to NL is RO and to NM is RP .

Substitute the respective values from the given values in the triangle,

`\sf:\implies (14)/(57)=(25)/(x) \\`

`\sf:\implies x = (25(57))/(14) \\`

`\sf:\implies x = 101.78 \\`

`\sf:\implies \red{ x = 101.8}\\`

Hence the value of x is 101.8 to the nearest tenth.

Answer 2

The length of line segment PR is 101.8 units (nearest tenth).

Explanation:

In similar triangles, corresponding sides are always in the same ratio.

Therefore, if triangle LMN is similar to triangle OPR then:

`\implies \sf LM:OP=MN:PR=LN:OR`

From inspection of the given triangles:

• MN = 25
• LN = 14
• PR = x
• OR = 57

Substitute these values into the relevant ratio:

`\implies \sf MN:PR=LN:OR`

`\implies 25:x=14:57`

`\implies (25)/(x)=(14)/(57)`

Cross multiply:

`\implies 25 \cdot 57=14 \cdot x`

`\implies 1425=14 x`

To solve for x, divide both sides by 14:

`\implies (1425)/(14)=(14x)/(14)`

`\implies x=101.785714...`

Therefore, the length of line segment PR is 101.8 units to the nearest tenth.