Question

The figures are similar. Find the missing length.Round to the nearest thousandth ​

Answer 1

The missing x = 0.675 m

Explanation:

In similar triangles, the corresponding sides are proportion (means their ratios are equal)

In the given figure

∵ The two triangles are similar

∴ Their corresponding sides are proportion

∵ The sides of lengths 1.8 m and x are corresponding sides

∵ The sides of lengths 8.0 m and 3.0 are corresponding sides

∴
`(1.8)/(x)` =
`(8.0)/(3.0)`

→ By using cross multiplication

∴ x × 8.0 = 1.8 × 3.0

∴ 8x = 5.4

→ Divide both sides by 8

∵
`(8x)/(8)` =
`(5.4)/(8)`

∴ x = 0.675

→ No rounding because there is no digit after the thousandth digit

∴ x = 0.675 m