Question

The perimeters of two similar triangles ABCand LMN are 60cm and 48cm respectively.If LM=8cm Find AB??

Answer 1

solution:

$let us the triangle ABC is similar to triangle LMN\\</p><p>so,\frac{AB}{LM}=\frac{BC}{MN}=\frac{AC}{LN}\\</p><p>therefore,\frac{AB}{8}=\frac{BC}{MN}=\frac{AC}{LN}---------(1)\\</p><p>Now,as\frac{BC}{MN}=\frac{AC}{LN}\\</p><p>therefore,\frac{BC}{AC}=\frac{MN}{LN}\\</p><p>by appling the componendo\\</p><p>\frac{BC+AC}{AC}=\frac{MN+LN}{LN}\\</p><p>\frac{(60-AB)}{AC}=\frac{(48-LM)}{LN}\\</p><p>\frac{(60-AB)}{AC}=\frac{40}{LN}\\</p><p>by cross multiplication,\\</p><p>\frac{(60-AB)}{40}=\frac{AC}{LN}$$\frac{(60-AB)}{40}=\frac{AB}{8} (from equation 1)\\</p><p>again,cross multiplication\\</p><p>480-8\times AB=40\times AB\\</p><p>480=48AB\\</p><p>AB=10$